In this thread, we post games that were THE first to do a particular thing. Not just one of the first, not just the one that popularized that thing, but THE first.
I've got a few here:
(NOTE: THE BELOW ARE OUTDATED.. Just keeping the original contents of this post for posterity.)
(NOTE: THE ABOVE EXAMPLES ARE OUTDATED. See below for up-to-date examples.)
EDIT: Okay, going to try to get everything confirmed to be first into one post here.
Omnibus list in chronological order
Shooter: Cathode Ray Tube Amusement Device (1947) or Spacewar (1962), depending on definition.
Video game: Cathode Ray Tube Amusement Device (1947)
Patent: Cathode Ray Tube Amusement Device (made in 1947, patented 1948)
Artificial intelligence: Nim (1951)
Turn-based strategy: Nim (1951)
In-game credits: OXO (1952)
Onscreen graphics: OXO (1952)
Gameplay in real time: Tennis for Two (1958)
Gravity physics: Tennis for Two (1958)
Side perspective: Tennis for Two (1958)
Simultaneous multiplayer: Tennis for Two (1958)
Sports game: Tennis for Two (1958)
Tennis: Tennis for Two (1958)
Shooting of onscreen enemies with onscreen projectiles: Spacewar (1962)
Teleportation: Spacewar (1962)
Video game console: Brown Box (1967)
In-game performance rating: Hamurabi (PDP-8, 1968)
Resource management: Hamurabi (PDP-8, 1968)
Exploration of environment spanning more than one screen: Space Travel (Multics, 1969) or Superman (Atari 2600, 1979), depending on definition.
Gravity exerted on movable player character: Space Travel (Multics, 1969) or Lunar Lander (PDP-8, 1969)
Open world: Space Travel (Multics, 1969)
Based on non-video game fictional property: Star Trek (SDS Sigma 7, 1971) [unlicensed]
Baseball: Baseball (PDP-10, 1971)
Coin-operated video game: Galaxy Game (1971)
Commercially-released video game: Computer Space (arcade, 1971)
In-game score counter: Computer Space (arcade, 1971)
Level background: Computer Space (arcade, 1971)
Season mode: Baseball (PDP-10, 1971)
Sound: Computer Space (arcade, 1971)
Video game company: Syzygy Engineering (1971)
Adventure game: Hunt the Wumpus (BASIC, code published in magazine, 1972) or Adventure (PDP-10, 1976), depending on definition.
Basketball: Basketball (Magnavox Odyssey, 1972)
Commercially-released video game console: Magnavox Odyssey (1972)
Game cartridges: Magnavox Odyssey (1972)
Home-to-arcade port: Pong (1972), unofficial arcade port of the Magnavox Odyssey (1972); Magnavox sued 1974; Atari settled out of court in 1976 by licensing the rights from Magnavox
Light gun: Magnavox Odyssey (1972)
Appearance in a movie: Soylent Green (1973) features Computer Space (arcade, 1971) in one scene.
Cheats: Maze War (PDS-1, 1973)
Cover system: Maze War (PDS-1, 1973) or Gun Fight (arcade, 1975), depending on definition.
Deathmatch: Maze War (PDS-1, 1973)
First-person perspective: Maze War (PDS-1, 1973)
First-person shooter: Maze War (PDS-1, 1973), Spasim (PLATO, 1974), Interceptor (arcade, 1975), or Battlezone (arcade, 1980), depending on definition.
In-game map: Maze War (PDS-1, 1973)
LAN support: Maze War (PDS-1, 1973)
Level editor: Maze War (PDS-1, 1973)
Organic characters onscreen: Maze War (PDS-1, 1973) [all players are giant eyeballs]
Racing game: Space Race (arcade, 1973)
Collecting onscreen objects in real time: Clean Sweep (arcade, 1974)
Driving game: Gran Trak 10 (arcade, 1974) or Speed Race (arcade, 1974)
Japanese game released in the United States: Speed Race (arcade, 1974)
Pinball sim: Pin Pong (arcade, 1974)
Online game: Maze War [1974 version] (PDP-10, 1974) [connected through ARPANET]
Arcade-to-home port: Atari/Sears Pong (dedicated console, 1975)
Boss battle: dnd (PLATO, 1975)
Color graphics without screen overlays: Indy 800 (arcade, 1975)
Dual-joystick controls: Gun Fight (arcade, 1975)
First-person gameplay in real time: Interceptor (arcade, 1975)
Flight sim: Interceptor (arcade, 1975)
Horse riding: Steeplechase (arcade, 1975)
In-game use of the phrase "Game Over": Gun Fight (arcade, 1975) [derives from pinball]
Jumping: Steeplechase (arcade, 1975)
Onscreen human: Gun Fight (arcade, 1975)
Onscreen human death: Gun Fight (arcade, 1975)
Programmed with microprocessor (earliest game able to be emulated, rather than simulated): Gun Fight [US version] (arcade, 1975)
RPG: dnd (PLATO, 1975), pedit5 (PLATO, 1975), or Dungeon (PDP-10, 1975)
Sales over 1 million units: Atari/Sears Pong (dedicated console, 1975)
Turret level: Anti-AIrcraft (arcade, 1975)
Underwater setting: Shark Jaws (arcade, 1975)
Vehicle as weapon: Destruction Derby (arcade, 1975)
Card game sim: Hit Me (arcade, 1976)
Controversy over violent content: Death Race (arcade, 1976)
Console with CPU: Fairchild Channel F (1976)
Destructible terrain: Either Breakout (arcade, 1976) [blocks] or Space Invaders (arcade, 1978) [barriers], depending on definition.
In-game use of phrase "high score": Sea Wolf (arcade, 1976) [derives from pinball]
Handheld game with microprocessor: Mattel Auto Race (1976)
Hand-to-hand combat: Heavyweight Champ (arcade, 1976)
Licensed from a non-video game property: Fonz (arcade, 1976)
Multiple lives in a single-player game: Breakout (arcade, 1976)
One-on-one fighting game: Heavyweight Champ (arcade, 1976), Warrior (arcade, 1979), or Karate (Atari 2600, 1982), depending on definition.
Rumble feature: Fonz (arcade, 1976)
Sprite scaling: Night Driver (arcade, 1976)
Clint-server online matchmaking: Maze War [1977 Xerox version] (Xerox Alto, 1977)
Compilation of older games on a single cartridge: Video Olympics (Atari 2600, 1977)
Scrolling: Super Bug (arcade, 1977)
Splitscreen multiplayer: Street Racer (Atari 2600, 1977)
Stealth mechanics: Combat [invisible tanks in tank mode, clouds in dogfighting mode] (Atari 2600, 1977)
Vector graphics: Maze War [1977 Imlacs version] (Imlacs, 1977)
Continuous music during gameplay: Space Invaders (arcade, 1978)
Dynamic soundtrack: Either Space Invaders (arcade, 1978) or: Frogger (arcade, 1981), depending on definition.
High score table saved between sessions: Space Invaders (arcade, 1978)
Musical gameplay: Simon (standalone handheld game, 1978) or Dance Aerobics (NES, 1987), depending on whether Simon is considered a video game.
MMORPG: MUD1 (PDP-10, 1978), Island of Kesmai (PC, 1985), or Neverwinter Nights (PC, 1991), depending on definition.
Randomly generated levels: Beneath Apple Manor (Apple II, 1978) or Maze Craze (Atari 2600, 1978), depending on release date.
Rear view driving: Night Driver (Atari 2600, 1978)
Video game-related book with sales over 1 million copies: "BASIC Computer Games" by David H. Ahl (1978)
Action-adventure: Superman (Atari 2600, 1979) or Adventure (Atari 2600, 1980), depending on definition.
Black character: Basketball (Atari 400/800, 1979)
Cutscene: Either Space Invaders Part II (arcade, 1979) or Sheriff (arcade, 1979). Term coined in 1987 by Ron Gilbert to describe scenes in Maniac Mansion (C64, 1987)
Enemies break into smaller enemies: Asteroids (arcade, 1979)
Flip-screen scrolling: Superman (Atari 2600, 1979)
Handheld system with removable cartridges: Microvision (1979)
Inverse kinematics: Warrior (arcade, 1979) [sword points]
Licensed from comic book: Superman (Atari 2600, 1979)
Microtransactions: Lunar Lander (arcade, 1979) or Lost Tomb (arcade, 1982), depending on definition.
Multiple language options: Sundance (arcade, 1979) [English or Japanese]
Name entry on high score table: Star Fire (arcade, 1979)
Pause button: Superman (Atari 2600, 1979)
Picking up and carrying objects in real time: Superman (Atari 2600, 1979)
Real movement on Z-axis: Speed Freak (arcade, 1979)
Scripted event in real time: Superman (Atari 2600, 1979) [Lex's henchmen blowing up bridge]
Sword combat in real time: Warrior (arcade, 1979)
Third-party developer for a home console: Activision (1979)
Third-person shooter: Radar Scope (arcade, 1979), Space Harrier (arcade, 1985), Silpheed (arcade, 1986), Contra (arcade, 1987) [base levels], or Devastators (arcade, 1988), depending on definition.
Vehicle with limited fuel: Lunar Lander (arcade, 1979)
Arbitrary movement in polygonal environment: Battlezone (arcade, 1980)
Boss battle in real time: Phoenix (arcade, 1980) [mothership]
Climbing up ledges: Space Panic (arcade, 1980) or Crazy Climber (arcade, 1980)
Designed and programmed by a woman: 3D Tic-Tac-Toe (Atari 2600, 1980) [Designer: Carol Shaw]
Digitized speech: Stratovox (arcade, 1980)
Easter egg: Adventure (Atari 2600, 1980)
Enemies can kill each other: Berzerk (arcade, 1980)
Events happen in real time outside player's view: Defender (arcade, 1980) or Rally-X (arcade, 1980)
Expansion pack: Either the first user-made module in Eamon (Apple II, 1980), or, if only official expansions count, Upper Reaches of Apshai (TRS-80, 1981) [Expansion to Temple of Apshai, from 1979]
Female player character: Kid Venture (Apple II, 1980)
Graphical adventure game: Mystery House (Apple II, 1980)
Known involvement in death of player: Berzerk (arcade, 1980)
Ladders: Space Panic (arcade, 1980)
Licensed athlete: Pele's Soccer (Atari 2600, 1980)
Licensed celebrity: Pele's Soccer (Atari 2600, 1980)
Parallax scrolling: Defender (arcade, 1980), Moon Patrol (arcade, 1982), or Jungle Hunt (arcade, 1982), depending on definition and release date.
Platforms: Space Panic (arcade, 1980)
Platform game: Space Panic (arcade, 1980), Jump Bug (arcade, 1981), or Donkey Kong (arcade, 1981), depending on definition and release date.
Power-up: Pac-Man (arcade, 1980)
Proprietary engine: Either Eamon (Apple II, 1980) or The Quill (ZX Spectrum, 1983), depending on definition.
Simultaneous co-op multiplayer: Rip-Off (arcade, 1980)
Smart bomb: Defender (arcade, 1980)
Bonus stage: Galaga (arcade, 1981)
Changing direction in mid-jump: Jump Bug (arcade, 1981)
Digital distribution service on a home console: PlayCable (Intellivision, 1981)
Hub world: Venture (arcade, 1981)
Licensed from a tabletop game: Dungeons & Dragons Computer Fantasy Game (handheld game, 1981)
Life bar: Scramble (arcade, 1981), Atic Atac (ZX Spectrum, 1983) or Gemstone Warrior (Apple II, 1984), depending on definition.
Minigame: Galaga (arcade, 1981) or Escape from the Mindmaster (Atari 2600, 1982), depending on definition.
Motion controller: Le Stick (Atari 2600, 1981)
Multiple party members in a role-playing game: Wizardry (Apple II, 1981)
Real-time strategy: Utopia (Intellivision, 1981), Bokosuka Wars (Sharp X1, 1983), or Stonkers (ZX Spectrum, 1983), depending on definition and release date.
Recruitable enemies: Galaga (arcade, 1981)
Released on multiple disks: Ulysses and the Golden Fleece (Apple II, 1981)
Scrolling platform game: Jump Bug (arcade, 1981), Moon Patrol (arcade, 1982), Major Havoc (arcade, 1983), or Snokie (Atari 400/800, 1983), depending on definition and release date.
Sexual content: Softporn Adventure (Apple II, 1981)
Stealth game: Castle Wolfenstein (Apple II, 1981) or 005 (arcade, 1981), depending on release date.
Video game magazine: Electronic Games (1981)
Action RPG: Dungeons of Daggorath (TRS-80, 1982), Bokosuka Wars (Sharp X1, 1983), The Tower of Druaga (arcade, 1984), Dragon Slayer (FM-7, 1984), or Hydlide (PC-88, 1984), depending on definition.
Billboard chart single about video games: "Pac-Man Fever" by Buckner & Garcia (1982, #9 peak)
Carry over save from previous game: Wizardry 2 (Apple II, 1982)
D-pad: Donkey Kong (Game & Watch, 1982)
Dialogue trees: Danchi Tsuma no Yuwaku (PC-88, 1982)
First-person melee combat in real time: Crypts of Chaos (Atari 2600, 1982) or Dungeon Master (Atari ST, 1987), depending on definition [Crypts of Chaos is supposed to be melee but looks like lasers]
Franchise mode: Football Manager (TRS-80, 1982)
Grappling hook: Spider-Man (Atari 2600, 1982) [web] or Raiders of the Lost Ark (Atari 2600, 1982)
Isometric perspective: Zaxxon (arcade, 1982)
Japanese RPG: The Dragon and Princess (PC-8001, 1982)
Jumping used to defeat enemies: Either Joust (arcade, 1982) or Horace and the Spiders (ZX Spectrum, 1983), depending on how jumping is defined.
Licensed song: Journey Escape (Atari 2600, 1982) [TIA rendition of "Don't Stop Believin'"]
Map included with game: Ultima II (Apple II, 1982)
Movie with plot centered around video games: Tron (1982)
Multiple endings: Deadline (Apple II, 1982)
Onscreen ejaculation: Beat 'Em and Eat 'Em (Atari 2600, 1982)
Product placement: Pole Position (arcade, 1982)
Stereoscopic 3D: Sub-Roc 3D (arcade, 1982)
Survival horror: Haunted House (Atari 2600, 1982) or Terror House (handheld game, 1982), depending on release date.
TV show based on a video game: Pac-Man (1982)
Zombies: Entombed (Atari 2600, 1982)
Beat 'em up: Attack of the Phantom Karate Devils (C64, 1983), Karateka (Apple II, 1984), or Kung Fu Master (arcade, 1984), depending on definition.
Chainsaw: The Texas Chainsaw Massacre (Atari 2600, 1983)
Cheat code: Manic Miner (ZX Spectrum, 1983)
Cheating device: The Great Escape Utility (Apple II, 1983); enables cheats in Castle Wolfenstein (Apple II, 1981)
Controlling jump height with length of button press: Major Havoc (arcade, 1983)
Day-night cycle: Forbidden Forest (C64, 1983) or Terror Daktil 4D (ZX Spectrum, 1983)
Filled polygonal graphics: I, Robot (arcade, 1983)
Isometric platform game: Congo Bongo (arcade, 1983) or Ant Attack (ZX Spectrum, 1983), depending on release date.
Jetpack: Jetpac (ZX Spectrum, 1983) or Kagirinaki Takatai (Sharp X1, 1983), depending on release date.
Live instrumentation: Journey (arcade, 1983) [cassette tape inside cabinet plays "Separate Ways" by Journey during ending]
Multidirectional arbitrary scrolling from side perspective: Major Havoc (arcade, 1983). If Major Havoc is disqualified due to being a vector game, then it's either Lode Runner (NES, 1984) [2 directions] or Dragon Buster (arcade, 1985) [8 directions].
Onscreen blood: Halloween (Atari 2600, 1983)
Point-and-click interface: Project Mephius (FM-7, 1983) [onscreen cursor controlled with keyboard]
Racing game with built-in track editor: Rally Speedway (Atari 400/800, 1983)
Quick time event: Either Dragon's Lair (arcade, 1983) or Die Hard Arcade (arcade, 1995), depending on definition.
Recording of licensed song: Journey (arcade, 1983) [their song "Separate Ways" plays from a cassette player inside the cabinet during the ending]
Released on optical disc: Astron Belt [Laserdisc] (arcade, 1983) or Dragon's Lair [Laserdisc] (arcade, 1983)
Run and gun: Hover Attack (Sharp X1, 1983)
Video games as product placement in movie: Joysticks (1983)
360-degree player movement on six axes: Elite (BBC Micro, 1984)
Boost pad: Excitebike (NES, 1984) or RC Pro-Am (NES, 1988), depending on definition.
Capture the flag: Bannercatch (Apple II, 1984)
Dating sim: Don Juan (Amstrad CPC, 1984)
Designer's name in title: John Chenault's Snake (PC, 1984) [box only] or Will Harvey's Music Construction Set (Apple II, 1984) [box and title screen]
Interactive title screen: Ghostbusters [press space to say "Ghostbusters!"] (C64, 1984)
In-game karaoke: Ghostbusters [title screen] (C64, 1984)
Live orchestral music: Firefox (arcade, 1984)
Mouse controls: Enchanted Scepter (Macintosh, 1984)
Password save: Hydlide (PC-88, 1984)
Profane speech sample: Oh Shit! (MSX, 1984) [voice says "oh shit!" when you die]
Profanity in title: Oh Shit! (MSX, 1984)
Published book on video game theory: "The Art of Computer Game Design", by Chris Crawford (1984)
Regenerating health: Hydlide (PC-88, 1984)
Separate music for boss fight: Hydlide (PC-88, 1984)
Crafting: Ultima IV (Apple II, 1985) features herb mixing; Feud (ZX Spectrum, 1987) made herb-mixing the central premise of the game.
Double jump: Dragon Buster (arcade, 1985)
In-game use of the term "1-up" to refer to extra lives: Super Mario Bros. (NES, 1985) [derives from pinball]
Usable toilet: Little Computer People (C64, 1985)
In-game use of the word "boss" to describe strong enemies: Renegade (arcade, 1986)
Vocal music during gameplay: Psycho Soldier (arcade, 1986)
LGBT character: Moonmist (PC, 1986)
3D proprietary engine: Freescape (Amstrad CPC, 1987); first used in Driller (Amstrad CPC, 1987)
Adjustable car radio during gameplay: Rad Racer (NES, 1987)
Charge shot: R-Type (arcade, 1987)
First-person multiplayer in real-time: MIDI Maze (Atari ST, 1987)
Interactive loading screen: Delta (C64, 1987)
Photography as gameplay: Bishoujo Shashinkan: Moving School (PC-88, 1987)
Save battery in cartridge: The Legend of Zelda [US version] (NES, 1987)
Team deathmatch: MIDI Maze (Atari ST, 1987)
Breeding: Eco (Atari ST, 1988)
First-person jumping: Dark Side (Atari ST, 1988) [jetpack] or Ultima Underworld (PC, 1992)
Loading screen minigame: Joe Blade 2 (ZX Spectrum, 1988) ["Invade-a-Load", a Pac-Man clone]
Online multiplayer with real time graphics: Air Warrior (PC, 1988)
Sticky grenade: Mega Man 2 (NES, 1988) or Shadow Warrior (PC, 1997), depending on definition.
Over-the-shoulder perspective: Dead Angle (arcade, 1988) or Dynamite Duke (arcade, 1989), depending on definition.
Released on CD-ROM: Fighting Street and No-Ri-Ko were both released for the launch of the PC Engine CD on December 4, 1988.
Live instrumentation on original soundtrack: Ys Book I&II (PC Engine, 1989) [electric guitar]
3D platform game: Alpha Waves (Atari ST, 1990)
Memory card on console: Neo Geo AES (1990)
Tower defense: Rampart (arcade, 1990)
Destructible terrain at pixel scale: Lemmings (Amiga, 1991) or Scorched Earth (PC, 1991)
Padlock view: Falcon 3.0 (PC, 1991)
Polygonal fighting game: 4D Boxing (PC, 1991). If boxing games don't count, then it's Virtua Fighter (arcade, 1993).
Circle-strafing: Gun Buster (arcade, 1992)
Gameplay recording: Stunt Island (PC, 1992)
Limb damage: UnReal World (PC.1992)
Limit break: Art of Fighting (arcade, 1992)
Secret super move (fighting games): Art of Fighting (arcade, 1992)
Taunt button: Art of Fighting (arcade, 1992)
Texture mapping: Ultima Underworld (PC, 1992)
Vertical free-look: Ultima Underworld (PC, 1992), CyClones (PC, 1994), or Marathon (Mac, 1994), depending on definition.
Voxels: Comanche (PC, 1992)
Collector's edition: Street Fighter II Turbo [PAL version] (SNES, 1993)
Individually rendered polygonal fingers: Virtua Fighter (arcade, 1993)
Movie based on a video game: Super Mario Bros. (1993)
Dolby Surround support: Super Turrican (SNES, 1993)
Destructible terrain with fluid physics: Clonk (PC, 1994)
Mobile game: Tetris (Hagenuk MT-2000, 1994)
Polygonal console game at 60fps: Geom Cube (PS1, 1994)
Voice chat: Marathon (Macintosh, 1994)
Per-frame resolution greater than 1 million pixels out-of-box: Cyberbykes (PC, 1995) [maximum resolution: 1280x1024]
Snapping to cover: Time Crisis (arcade, 1995) or Winback (N64, 1999), depending on definition.
African-developed video game released internationally: Toxic Bunny (PC, 1996)
Instanced quests in MMO: The Realm Online (PC, 1996)
1080p+ support out-of-box: Total Annihilation (PC, 1997)
Retail game rated AO by ESRB: Riana Rouge (PC, 1997)
Sniper rifle scope with arbitrary zooming: MDK (PC, 1997)
Bump-mapping: Montezuma's Return (PC, 1997/1998 [release date not clear]) or Unreal (PC, 1998)
MOBA: Aeon of Strife [Starcraft custom map] (PC, 1998)
Ragdoll physics: Jurassic Park: Trespasser (PC, 1998)
Game of the Year re-release: Half-Life: Game of the Year Edition (PC, 1999)
Bloom lighting: Ico (PS2, 2001)
1080i support out-of-box on console: Dragon's Lair 3D (Xbox, 2002)
Game soundtrack certified platinum by RIAA: NBA Live 2003 (PS2/Xbox/GameCube, 2002)
Paid DLC: Mechassault (Xbox, 2002)
Published video game poetry collection: "Blue Wizard is About to Die!" by Seth Flynn Barkan (2004)
Grammy-winning (and nominated) original video game song: "Baba Yetu" from Civilization IV (PC, 2005) [awarded in 2011]
Screen space ambient occlusion: Crysis (PC, 2007)
Cloud gaming service: OnLive (2010)
Licensing of fan translation for official release: Ys: The Oath in Felghana [US version] (PSP, 2010)
Grammy-winning video game soundtrack: Journey (PS3, 2012)
Categorical list is a few posts below.
I've got a few here:
(NOTE: THE BELOW ARE OUTDATED.. Just keeping the original contents of this post for posterity.)
Computer Space (arcade, 1971) was the first commercially-released video game: http://www.youtube.com/watch?v=b3BQsCCwo8w
Gun Fight (arcade, 1975) was the first video game to contain a microprocessor, and therefore the earliest game that can be emulated, rather than simulated: https://www.youtube.com/watch?v=xYa0G6KGayk
Fonz (arcade, 1976) was the first game licensed from a non-video game property, and the first game with a rumble feature: http://en.wikipedia.org/wiki/Fonz_(video_game)
Super Bug (arcade, 1977) was the first game with scrolling: https://www.youtube.com/watch?v=N61Lacr9IGs
Space Invaders (arcade, 1978) was the first game to give the player multiple lives, and the first to have continuous music during gameplay: http://www.youtube.com/watch?v=437Ld_rKM2s
Superman (Atari 2600, 1979) was the first game licensed from a comic book: https://www.youtube.com/watch?v=r7U2TFIayos
I, Robot (arcade, 1983) was the first game to use filled polygon graphics: https://www.youtube.com/watch?v=gmvWxG2zvs8
Dragon's Lair (arcade, 1983) was the first commercially-released game on Laserdisc, and thus the first game on any kind of optical disc: https://www.youtube.com/watch?v=i6em4GRiRY0
Dragon Buster (arcade, 1984) was the first game to feature a life bar, and the first to feature a double jump: https://www.youtube.com/watch?v=OIAU4EYfGXM
Fighting Street (https://www.youtube.com/watch?v=MTlzvVm_Nvk) and No-Ri-Ko (https://www.youtube.com/watch?v=0oidyRt3RNk), both released on December 4, 1988, at the launch of the PC Engine CD, were the first video games on CD-ROM.
And this one's not a game, but a service: GameLine for the Atari 2600 (1983) was the first digital distribution service on consoles: http://en.wikipedia.org/wiki/Gameline
I believe all of the above are correct, but I'd love to be proven wrong.
Post more!
Gun Fight (arcade, 1975) was the first video game to contain a microprocessor, and therefore the earliest game that can be emulated, rather than simulated: https://www.youtube.com/watch?v=xYa0G6KGayk
Fonz (arcade, 1976) was the first game licensed from a non-video game property, and the first game with a rumble feature: http://en.wikipedia.org/wiki/Fonz_(video_game)
Super Bug (arcade, 1977) was the first game with scrolling: https://www.youtube.com/watch?v=N61Lacr9IGs
Space Invaders (arcade, 1978) was the first game to give the player multiple lives, and the first to have continuous music during gameplay: http://www.youtube.com/watch?v=437Ld_rKM2s
Superman (Atari 2600, 1979) was the first game licensed from a comic book: https://www.youtube.com/watch?v=r7U2TFIayos
I, Robot (arcade, 1983) was the first game to use filled polygon graphics: https://www.youtube.com/watch?v=gmvWxG2zvs8
Dragon's Lair (arcade, 1983) was the first commercially-released game on Laserdisc, and thus the first game on any kind of optical disc: https://www.youtube.com/watch?v=i6em4GRiRY0
Dragon Buster (arcade, 1984) was the first game to feature a life bar, and the first to feature a double jump: https://www.youtube.com/watch?v=OIAU4EYfGXM
Fighting Street (https://www.youtube.com/watch?v=MTlzvVm_Nvk) and No-Ri-Ko (https://www.youtube.com/watch?v=0oidyRt3RNk), both released on December 4, 1988, at the launch of the PC Engine CD, were the first video games on CD-ROM.
And this one's not a game, but a service: GameLine for the Atari 2600 (1983) was the first digital distribution service on consoles: http://en.wikipedia.org/wiki/Gameline
I believe all of the above are correct, but I'd love to be proven wrong.
Post more!
(NOTE: THE ABOVE EXAMPLES ARE OUTDATED. See below for up-to-date examples.)
EDIT: Okay, going to try to get everything confirmed to be first into one post here.
Omnibus list in chronological order
Shooter: Cathode Ray Tube Amusement Device (1947) or Spacewar (1962), depending on definition.
Video game: Cathode Ray Tube Amusement Device (1947)
Patent: Cathode Ray Tube Amusement Device (made in 1947, patented 1948)
Artificial intelligence: Nim (1951)
Turn-based strategy: Nim (1951)
In-game credits: OXO (1952)
Onscreen graphics: OXO (1952)
Gameplay in real time: Tennis for Two (1958)
Gravity physics: Tennis for Two (1958)
Side perspective: Tennis for Two (1958)
Simultaneous multiplayer: Tennis for Two (1958)
Sports game: Tennis for Two (1958)
Tennis: Tennis for Two (1958)
Shooting of onscreen enemies with onscreen projectiles: Spacewar (1962)
Teleportation: Spacewar (1962)
Video game console: Brown Box (1967)
In-game performance rating: Hamurabi (PDP-8, 1968)
Resource management: Hamurabi (PDP-8, 1968)
Exploration of environment spanning more than one screen: Space Travel (Multics, 1969) or Superman (Atari 2600, 1979), depending on definition.
Gravity exerted on movable player character: Space Travel (Multics, 1969) or Lunar Lander (PDP-8, 1969)
Open world: Space Travel (Multics, 1969)
Based on non-video game fictional property: Star Trek (SDS Sigma 7, 1971) [unlicensed]
Baseball: Baseball (PDP-10, 1971)
Coin-operated video game: Galaxy Game (1971)
Commercially-released video game: Computer Space (arcade, 1971)
In-game score counter: Computer Space (arcade, 1971)
Level background: Computer Space (arcade, 1971)
Season mode: Baseball (PDP-10, 1971)
Sound: Computer Space (arcade, 1971)
Video game company: Syzygy Engineering (1971)
Adventure game: Hunt the Wumpus (BASIC, code published in magazine, 1972) or Adventure (PDP-10, 1976), depending on definition.
Basketball: Basketball (Magnavox Odyssey, 1972)
Commercially-released video game console: Magnavox Odyssey (1972)
Game cartridges: Magnavox Odyssey (1972)
Home-to-arcade port: Pong (1972), unofficial arcade port of the Magnavox Odyssey (1972); Magnavox sued 1974; Atari settled out of court in 1976 by licensing the rights from Magnavox
Light gun: Magnavox Odyssey (1972)
Appearance in a movie: Soylent Green (1973) features Computer Space (arcade, 1971) in one scene.
Cheats: Maze War (PDS-1, 1973)
Cover system: Maze War (PDS-1, 1973) or Gun Fight (arcade, 1975), depending on definition.
Deathmatch: Maze War (PDS-1, 1973)
First-person perspective: Maze War (PDS-1, 1973)
First-person shooter: Maze War (PDS-1, 1973), Spasim (PLATO, 1974), Interceptor (arcade, 1975), or Battlezone (arcade, 1980), depending on definition.
In-game map: Maze War (PDS-1, 1973)
LAN support: Maze War (PDS-1, 1973)
Level editor: Maze War (PDS-1, 1973)
Organic characters onscreen: Maze War (PDS-1, 1973) [all players are giant eyeballs]
Racing game: Space Race (arcade, 1973)
Collecting onscreen objects in real time: Clean Sweep (arcade, 1974)
Driving game: Gran Trak 10 (arcade, 1974) or Speed Race (arcade, 1974)
Japanese game released in the United States: Speed Race (arcade, 1974)
Pinball sim: Pin Pong (arcade, 1974)
Online game: Maze War [1974 version] (PDP-10, 1974) [connected through ARPANET]
Arcade-to-home port: Atari/Sears Pong (dedicated console, 1975)
Boss battle: dnd (PLATO, 1975)
Color graphics without screen overlays: Indy 800 (arcade, 1975)
Dual-joystick controls: Gun Fight (arcade, 1975)
First-person gameplay in real time: Interceptor (arcade, 1975)
Flight sim: Interceptor (arcade, 1975)
Horse riding: Steeplechase (arcade, 1975)
In-game use of the phrase "Game Over": Gun Fight (arcade, 1975) [derives from pinball]
Jumping: Steeplechase (arcade, 1975)
Onscreen human: Gun Fight (arcade, 1975)
Onscreen human death: Gun Fight (arcade, 1975)
Programmed with microprocessor (earliest game able to be emulated, rather than simulated): Gun Fight [US version] (arcade, 1975)
RPG: dnd (PLATO, 1975), pedit5 (PLATO, 1975), or Dungeon (PDP-10, 1975)
Sales over 1 million units: Atari/Sears Pong (dedicated console, 1975)
Turret level: Anti-AIrcraft (arcade, 1975)
Underwater setting: Shark Jaws (arcade, 1975)
Vehicle as weapon: Destruction Derby (arcade, 1975)
Card game sim: Hit Me (arcade, 1976)
Controversy over violent content: Death Race (arcade, 1976)
Console with CPU: Fairchild Channel F (1976)
Destructible terrain: Either Breakout (arcade, 1976) [blocks] or Space Invaders (arcade, 1978) [barriers], depending on definition.
In-game use of phrase "high score": Sea Wolf (arcade, 1976) [derives from pinball]
Handheld game with microprocessor: Mattel Auto Race (1976)
Hand-to-hand combat: Heavyweight Champ (arcade, 1976)
Licensed from a non-video game property: Fonz (arcade, 1976)
Multiple lives in a single-player game: Breakout (arcade, 1976)
One-on-one fighting game: Heavyweight Champ (arcade, 1976), Warrior (arcade, 1979), or Karate (Atari 2600, 1982), depending on definition.
Rumble feature: Fonz (arcade, 1976)
Sprite scaling: Night Driver (arcade, 1976)
Clint-server online matchmaking: Maze War [1977 Xerox version] (Xerox Alto, 1977)
Compilation of older games on a single cartridge: Video Olympics (Atari 2600, 1977)
Scrolling: Super Bug (arcade, 1977)
Splitscreen multiplayer: Street Racer (Atari 2600, 1977)
Stealth mechanics: Combat [invisible tanks in tank mode, clouds in dogfighting mode] (Atari 2600, 1977)
Vector graphics: Maze War [1977 Imlacs version] (Imlacs, 1977)
Continuous music during gameplay: Space Invaders (arcade, 1978)
Dynamic soundtrack: Either Space Invaders (arcade, 1978) or: Frogger (arcade, 1981), depending on definition.
High score table saved between sessions: Space Invaders (arcade, 1978)
Musical gameplay: Simon (standalone handheld game, 1978) or Dance Aerobics (NES, 1987), depending on whether Simon is considered a video game.
MMORPG: MUD1 (PDP-10, 1978), Island of Kesmai (PC, 1985), or Neverwinter Nights (PC, 1991), depending on definition.
Randomly generated levels: Beneath Apple Manor (Apple II, 1978) or Maze Craze (Atari 2600, 1978), depending on release date.
Rear view driving: Night Driver (Atari 2600, 1978)
Video game-related book with sales over 1 million copies: "BASIC Computer Games" by David H. Ahl (1978)
Action-adventure: Superman (Atari 2600, 1979) or Adventure (Atari 2600, 1980), depending on definition.
Black character: Basketball (Atari 400/800, 1979)
Cutscene: Either Space Invaders Part II (arcade, 1979) or Sheriff (arcade, 1979). Term coined in 1987 by Ron Gilbert to describe scenes in Maniac Mansion (C64, 1987)
Enemies break into smaller enemies: Asteroids (arcade, 1979)
Flip-screen scrolling: Superman (Atari 2600, 1979)
Handheld system with removable cartridges: Microvision (1979)
Inverse kinematics: Warrior (arcade, 1979) [sword points]
Licensed from comic book: Superman (Atari 2600, 1979)
Microtransactions: Lunar Lander (arcade, 1979) or Lost Tomb (arcade, 1982), depending on definition.
Multiple language options: Sundance (arcade, 1979) [English or Japanese]
Name entry on high score table: Star Fire (arcade, 1979)
Pause button: Superman (Atari 2600, 1979)
Picking up and carrying objects in real time: Superman (Atari 2600, 1979)
Real movement on Z-axis: Speed Freak (arcade, 1979)
Scripted event in real time: Superman (Atari 2600, 1979) [Lex's henchmen blowing up bridge]
Sword combat in real time: Warrior (arcade, 1979)
Third-party developer for a home console: Activision (1979)
Third-person shooter: Radar Scope (arcade, 1979), Space Harrier (arcade, 1985), Silpheed (arcade, 1986), Contra (arcade, 1987) [base levels], or Devastators (arcade, 1988), depending on definition.
Vehicle with limited fuel: Lunar Lander (arcade, 1979)
Arbitrary movement in polygonal environment: Battlezone (arcade, 1980)
Boss battle in real time: Phoenix (arcade, 1980) [mothership]
Climbing up ledges: Space Panic (arcade, 1980) or Crazy Climber (arcade, 1980)
Designed and programmed by a woman: 3D Tic-Tac-Toe (Atari 2600, 1980) [Designer: Carol Shaw]
Digitized speech: Stratovox (arcade, 1980)
Easter egg: Adventure (Atari 2600, 1980)
Enemies can kill each other: Berzerk (arcade, 1980)
Events happen in real time outside player's view: Defender (arcade, 1980) or Rally-X (arcade, 1980)
Expansion pack: Either the first user-made module in Eamon (Apple II, 1980), or, if only official expansions count, Upper Reaches of Apshai (TRS-80, 1981) [Expansion to Temple of Apshai, from 1979]
Female player character: Kid Venture (Apple II, 1980)
Graphical adventure game: Mystery House (Apple II, 1980)
Known involvement in death of player: Berzerk (arcade, 1980)
Ladders: Space Panic (arcade, 1980)
Licensed athlete: Pele's Soccer (Atari 2600, 1980)
Licensed celebrity: Pele's Soccer (Atari 2600, 1980)
Parallax scrolling: Defender (arcade, 1980), Moon Patrol (arcade, 1982), or Jungle Hunt (arcade, 1982), depending on definition and release date.
Platforms: Space Panic (arcade, 1980)
Platform game: Space Panic (arcade, 1980), Jump Bug (arcade, 1981), or Donkey Kong (arcade, 1981), depending on definition and release date.
Power-up: Pac-Man (arcade, 1980)
Proprietary engine: Either Eamon (Apple II, 1980) or The Quill (ZX Spectrum, 1983), depending on definition.
Simultaneous co-op multiplayer: Rip-Off (arcade, 1980)
Smart bomb: Defender (arcade, 1980)
Bonus stage: Galaga (arcade, 1981)
Changing direction in mid-jump: Jump Bug (arcade, 1981)
Digital distribution service on a home console: PlayCable (Intellivision, 1981)
Hub world: Venture (arcade, 1981)
Licensed from a tabletop game: Dungeons & Dragons Computer Fantasy Game (handheld game, 1981)
Life bar: Scramble (arcade, 1981), Atic Atac (ZX Spectrum, 1983) or Gemstone Warrior (Apple II, 1984), depending on definition.
Minigame: Galaga (arcade, 1981) or Escape from the Mindmaster (Atari 2600, 1982), depending on definition.
Motion controller: Le Stick (Atari 2600, 1981)
Multiple party members in a role-playing game: Wizardry (Apple II, 1981)
Real-time strategy: Utopia (Intellivision, 1981), Bokosuka Wars (Sharp X1, 1983), or Stonkers (ZX Spectrum, 1983), depending on definition and release date.
Recruitable enemies: Galaga (arcade, 1981)
Released on multiple disks: Ulysses and the Golden Fleece (Apple II, 1981)
Scrolling platform game: Jump Bug (arcade, 1981), Moon Patrol (arcade, 1982), Major Havoc (arcade, 1983), or Snokie (Atari 400/800, 1983), depending on definition and release date.
Sexual content: Softporn Adventure (Apple II, 1981)
Stealth game: Castle Wolfenstein (Apple II, 1981) or 005 (arcade, 1981), depending on release date.
Video game magazine: Electronic Games (1981)
Action RPG: Dungeons of Daggorath (TRS-80, 1982), Bokosuka Wars (Sharp X1, 1983), The Tower of Druaga (arcade, 1984), Dragon Slayer (FM-7, 1984), or Hydlide (PC-88, 1984), depending on definition.
Billboard chart single about video games: "Pac-Man Fever" by Buckner & Garcia (1982, #9 peak)
Carry over save from previous game: Wizardry 2 (Apple II, 1982)
D-pad: Donkey Kong (Game & Watch, 1982)
Dialogue trees: Danchi Tsuma no Yuwaku (PC-88, 1982)
First-person melee combat in real time: Crypts of Chaos (Atari 2600, 1982) or Dungeon Master (Atari ST, 1987), depending on definition [Crypts of Chaos is supposed to be melee but looks like lasers]
Franchise mode: Football Manager (TRS-80, 1982)
Grappling hook: Spider-Man (Atari 2600, 1982) [web] or Raiders of the Lost Ark (Atari 2600, 1982)
Isometric perspective: Zaxxon (arcade, 1982)
Japanese RPG: The Dragon and Princess (PC-8001, 1982)
Jumping used to defeat enemies: Either Joust (arcade, 1982) or Horace and the Spiders (ZX Spectrum, 1983), depending on how jumping is defined.
Licensed song: Journey Escape (Atari 2600, 1982) [TIA rendition of "Don't Stop Believin'"]
Map included with game: Ultima II (Apple II, 1982)
Movie with plot centered around video games: Tron (1982)
Multiple endings: Deadline (Apple II, 1982)
Onscreen ejaculation: Beat 'Em and Eat 'Em (Atari 2600, 1982)
Product placement: Pole Position (arcade, 1982)
Stereoscopic 3D: Sub-Roc 3D (arcade, 1982)
Survival horror: Haunted House (Atari 2600, 1982) or Terror House (handheld game, 1982), depending on release date.
TV show based on a video game: Pac-Man (1982)
Zombies: Entombed (Atari 2600, 1982)
Beat 'em up: Attack of the Phantom Karate Devils (C64, 1983), Karateka (Apple II, 1984), or Kung Fu Master (arcade, 1984), depending on definition.
Chainsaw: The Texas Chainsaw Massacre (Atari 2600, 1983)
Cheat code: Manic Miner (ZX Spectrum, 1983)
Cheating device: The Great Escape Utility (Apple II, 1983); enables cheats in Castle Wolfenstein (Apple II, 1981)
Controlling jump height with length of button press: Major Havoc (arcade, 1983)
Day-night cycle: Forbidden Forest (C64, 1983) or Terror Daktil 4D (ZX Spectrum, 1983)
Filled polygonal graphics: I, Robot (arcade, 1983)
Isometric platform game: Congo Bongo (arcade, 1983) or Ant Attack (ZX Spectrum, 1983), depending on release date.
Jetpack: Jetpac (ZX Spectrum, 1983) or Kagirinaki Takatai (Sharp X1, 1983), depending on release date.
Live instrumentation: Journey (arcade, 1983) [cassette tape inside cabinet plays "Separate Ways" by Journey during ending]
Multidirectional arbitrary scrolling from side perspective: Major Havoc (arcade, 1983). If Major Havoc is disqualified due to being a vector game, then it's either Lode Runner (NES, 1984) [2 directions] or Dragon Buster (arcade, 1985) [8 directions].
Onscreen blood: Halloween (Atari 2600, 1983)
Point-and-click interface: Project Mephius (FM-7, 1983) [onscreen cursor controlled with keyboard]
Racing game with built-in track editor: Rally Speedway (Atari 400/800, 1983)
Quick time event: Either Dragon's Lair (arcade, 1983) or Die Hard Arcade (arcade, 1995), depending on definition.
Recording of licensed song: Journey (arcade, 1983) [their song "Separate Ways" plays from a cassette player inside the cabinet during the ending]
Released on optical disc: Astron Belt [Laserdisc] (arcade, 1983) or Dragon's Lair [Laserdisc] (arcade, 1983)
Run and gun: Hover Attack (Sharp X1, 1983)
Video games as product placement in movie: Joysticks (1983)
360-degree player movement on six axes: Elite (BBC Micro, 1984)
Boost pad: Excitebike (NES, 1984) or RC Pro-Am (NES, 1988), depending on definition.
Capture the flag: Bannercatch (Apple II, 1984)
Dating sim: Don Juan (Amstrad CPC, 1984)
Designer's name in title: John Chenault's Snake (PC, 1984) [box only] or Will Harvey's Music Construction Set (Apple II, 1984) [box and title screen]
Interactive title screen: Ghostbusters [press space to say "Ghostbusters!"] (C64, 1984)
In-game karaoke: Ghostbusters [title screen] (C64, 1984)
Live orchestral music: Firefox (arcade, 1984)
Mouse controls: Enchanted Scepter (Macintosh, 1984)
Password save: Hydlide (PC-88, 1984)
Profane speech sample: Oh Shit! (MSX, 1984) [voice says "oh shit!" when you die]
Profanity in title: Oh Shit! (MSX, 1984)
Published book on video game theory: "The Art of Computer Game Design", by Chris Crawford (1984)
Regenerating health: Hydlide (PC-88, 1984)
Separate music for boss fight: Hydlide (PC-88, 1984)
Crafting: Ultima IV (Apple II, 1985) features herb mixing; Feud (ZX Spectrum, 1987) made herb-mixing the central premise of the game.
Double jump: Dragon Buster (arcade, 1985)
In-game use of the term "1-up" to refer to extra lives: Super Mario Bros. (NES, 1985) [derives from pinball]
Usable toilet: Little Computer People (C64, 1985)
In-game use of the word "boss" to describe strong enemies: Renegade (arcade, 1986)
Vocal music during gameplay: Psycho Soldier (arcade, 1986)
LGBT character: Moonmist (PC, 1986)
3D proprietary engine: Freescape (Amstrad CPC, 1987); first used in Driller (Amstrad CPC, 1987)
Adjustable car radio during gameplay: Rad Racer (NES, 1987)
Charge shot: R-Type (arcade, 1987)
First-person multiplayer in real-time: MIDI Maze (Atari ST, 1987)
Interactive loading screen: Delta (C64, 1987)
Photography as gameplay: Bishoujo Shashinkan: Moving School (PC-88, 1987)
Save battery in cartridge: The Legend of Zelda [US version] (NES, 1987)
Team deathmatch: MIDI Maze (Atari ST, 1987)
Breeding: Eco (Atari ST, 1988)
First-person jumping: Dark Side (Atari ST, 1988) [jetpack] or Ultima Underworld (PC, 1992)
Loading screen minigame: Joe Blade 2 (ZX Spectrum, 1988) ["Invade-a-Load", a Pac-Man clone]
Online multiplayer with real time graphics: Air Warrior (PC, 1988)
Sticky grenade: Mega Man 2 (NES, 1988) or Shadow Warrior (PC, 1997), depending on definition.
Over-the-shoulder perspective: Dead Angle (arcade, 1988) or Dynamite Duke (arcade, 1989), depending on definition.
Released on CD-ROM: Fighting Street and No-Ri-Ko were both released for the launch of the PC Engine CD on December 4, 1988.
Live instrumentation on original soundtrack: Ys Book I&II (PC Engine, 1989) [electric guitar]
3D platform game: Alpha Waves (Atari ST, 1990)
Memory card on console: Neo Geo AES (1990)
Tower defense: Rampart (arcade, 1990)
Destructible terrain at pixel scale: Lemmings (Amiga, 1991) or Scorched Earth (PC, 1991)
Padlock view: Falcon 3.0 (PC, 1991)
Polygonal fighting game: 4D Boxing (PC, 1991). If boxing games don't count, then it's Virtua Fighter (arcade, 1993).
Circle-strafing: Gun Buster (arcade, 1992)
Gameplay recording: Stunt Island (PC, 1992)
Limb damage: UnReal World (PC.1992)
Limit break: Art of Fighting (arcade, 1992)
Secret super move (fighting games): Art of Fighting (arcade, 1992)
Taunt button: Art of Fighting (arcade, 1992)
Texture mapping: Ultima Underworld (PC, 1992)
Vertical free-look: Ultima Underworld (PC, 1992), CyClones (PC, 1994), or Marathon (Mac, 1994), depending on definition.
Voxels: Comanche (PC, 1992)
Collector's edition: Street Fighter II Turbo [PAL version] (SNES, 1993)
Individually rendered polygonal fingers: Virtua Fighter (arcade, 1993)
Movie based on a video game: Super Mario Bros. (1993)
Dolby Surround support: Super Turrican (SNES, 1993)
Destructible terrain with fluid physics: Clonk (PC, 1994)
Mobile game: Tetris (Hagenuk MT-2000, 1994)
Polygonal console game at 60fps: Geom Cube (PS1, 1994)
Voice chat: Marathon (Macintosh, 1994)
Per-frame resolution greater than 1 million pixels out-of-box: Cyberbykes (PC, 1995) [maximum resolution: 1280x1024]
Snapping to cover: Time Crisis (arcade, 1995) or Winback (N64, 1999), depending on definition.
African-developed video game released internationally: Toxic Bunny (PC, 1996)
Instanced quests in MMO: The Realm Online (PC, 1996)
1080p+ support out-of-box: Total Annihilation (PC, 1997)
Retail game rated AO by ESRB: Riana Rouge (PC, 1997)
Sniper rifle scope with arbitrary zooming: MDK (PC, 1997)
Bump-mapping: Montezuma's Return (PC, 1997/1998 [release date not clear]) or Unreal (PC, 1998)
MOBA: Aeon of Strife [Starcraft custom map] (PC, 1998)
Ragdoll physics: Jurassic Park: Trespasser (PC, 1998)
Game of the Year re-release: Half-Life: Game of the Year Edition (PC, 1999)
Bloom lighting: Ico (PS2, 2001)
1080i support out-of-box on console: Dragon's Lair 3D (Xbox, 2002)
Game soundtrack certified platinum by RIAA: NBA Live 2003 (PS2/Xbox/GameCube, 2002)
Paid DLC: Mechassault (Xbox, 2002)
Published video game poetry collection: "Blue Wizard is About to Die!" by Seth Flynn Barkan (2004)
Grammy-winning (and nominated) original video game song: "Baba Yetu" from Civilization IV (PC, 2005) [awarded in 2011]
Screen space ambient occlusion: Crysis (PC, 2007)
Cloud gaming service: OnLive (2010)
Licensing of fan translation for official release: Ys: The Oath in Felghana [US version] (PSP, 2010)
Grammy-winning video game soundtrack: Journey (PS3, 2012)
Categorical list is a few posts below.
It was immensely influential though.
