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[StoveOven]

NES - Super Mario Bros.

SNES - Super Mario World
Genesis - Sonic the Hedgehog

N64 - Goldeneye 007 (probably the toughest for me to answer. Mario 64 and Ocarina of Time are both close runners up.)
Saturn - Virtua Fighter
PlayStation - Crash Bandicoot

Gamecube - Super Smash Bros. Melee
Dreamcast - Soul Caliber (People saying Shenmue are crazy.)
PlayStation 2 - Grand Theft Auto: San Andreas
Xbox - Halo: Combat Evolved

Wii - Wii Sports
PlayStation 3 - Uncharted 2: Among Thieves (GT5 and God of War 3 were bigger deals when they came out, but I don't think they are remembered in the same way.)
Xbox 360 - Grand Theft Auto V (Gears of War for exclusives)

Wii U - Splatoon
PlayStation 4 - Uncharted 4
Xbox One -

Game Boy - Tetris
Game Boy Advance - Pokemon Ruby/Sapphire
Nintendo DS - Nintendogs
Nintendo 3DS - Fire Emblem Awakening (Obviously not the biggest game on the system, but it made this franchise more relevant in the west than anyone thought it would ever be.)

PSP - Monster Hunter Portable 3rd
Vita - Persona 4 Golden

 

[ULTROS!]

SNES - Final Fantasy VI
PS1 - Final Fantasy VII
PS2 - Final Fantasy X
PS3 - Final Fantasy XIII
PS4 - Final Fantasy XV
PSVita - Danganronpa
PSP - Crisis Core: Final Fantasy VII
NDS - Ace Attorney: Phoenix Wright
3DS - Theatrhythm: Final Fantasy

 

[Pandy]

Updated the OP to reflect the answers in the thread. Thanks to everyone who contributed!

For the most part the changes were very straight-forward, and were for games that had come up during my initial thoughts for the thread. The close runs were for related games on the same system, such versions of GTA on PS2 or Naughty Dog games on PS3.

Still some odd answers in there I would say, but I was either out-numbered or with the more niche platforms/games I have no idea about them to contradict. If there's something on the list you disagree with then feel free to suggest a better alternative.

 

[inpHilltr8r]

BBC Micro - Elite

 

[Goldenroad]

From what I've owned:

Atari 2600 - Ms. Pacman
NES - Super Mario Brothers 3
SNES - Legend of Zelda: A Link to the Past
N64 - Goldeneye
PS1 - Metal Gear Solid
PS2 - GTA: San Andreas
Gamecube - Resident Evil 4
XBOX - Halo: CE
XBOX 360 - Call of Duty 4
PS3 - Uncharted 2
Wii - Wii Sports
Wii U - Super Mario Maker
PS4 - Rocket League
For fun: PC - Doom

 

[Nestunt]

Genesis - Sonic 2
Gameboy Colour - Pokemon Red
Playstation 1 - Final Fantasy VII
Playstation 2 - Grand Theft Auto III
Xbox - Tom Clancy's Splinter Cell
Xbox 360 - Call of Duty 4
PS4 - The Witcher 3

 

[Crixus]

For zx spectrum I'm torn between Saboteur and Dizzy.

 

[petran79]

Amiga: Kick Off 2 (tournaments are still taking place)
Master System: Alex Kid in Miracle World
Gameboy: Super Mario Land
NES: Ice Climber
SNES: Super Metroid
Nintendo64: Ocarina of Time
Gamecube: Metroid Prime
Dreamcast: Jet Set Radio
Mega Drive: Sonic the Hedgehog
Playstation: SOTN
PS2: Winning Eleven
PS3: GOW3
Xbox360: SF4

Windows 3: Indiana Jones Desktop adventures
DOS: Super EF2000 with Tactcom
Windows 95: Creatures

 

[CrashPrime]

Hard to argue with that list. My few alterations and variations:

Neo Geo – Metal Slug

Probably no better/worse than your choice but it is my first pick.

NES – Super Mario Bros. 3

I mean, a hollywood movie that was basically an infomercial?

WiiU – Super Smash Bros. U

Splatoon was great, but SSBU was basically -THE- game that supported Amiibo's and technically Amiibo's wouldn't qualify to define the system.

PS2 – Gran Turismo 3 A-Spec

I gotta go GT3 over GTA3. It might be because GTA3 was ported to so many other platforms that I just don't look at it as a PS2 title as much of a "everything" title at this point. Still awesome tho.

Dreamcast – Marvel vs. Capcom 2

It suffers some of the port challenges that GTA3 does in terms of being "Dreamcast", but damn if I and many others owned the system JUST for Mahvel. The beep from a dead VMU battery just puts me in the mood for optic blast.

PC - Doom

Half-Life vs. Doom. Coke vs. Pepsi. The only reason I go Doom is it seems they intend on keeping it alive and well.

Spoiler

Dear Lord Gaben, in Episode 3 we trust. Amen.

 

[Gozert]

More good picks. I went with Pokemon on GBC because that's how remember playing the game, so I don't really associate the games with the OG Game Boy.

Pokémon Red and Blue did come out before the Game Boy Color and have no added Game Boy Color features beyond a default color pallet which a lot of other "grey cart" Game Boy games also had. It also just had the normal Game Boy logo on the box rather than the Game Boy Color logo Gold and Silver had.

However, Game Boy and Game Boy Color have always been a bit tricky, because of the backwards and forewards compatibility and the relatively minor upgrade. Even Nintendo just lumps them together in their best selling software charts.

I think PC is an interesting one. I didn't put a pick down because I was torn between the idea of World of Warcraft, which I think would be the 'normal' gaming pick, and something like Mine Sweeper, which would probably be the first thing my non-gaming elders would think of. LoL didn't even occur to me, even though it's obviously massive.

PC is tricky indeed, because it has a much longer lifespan than any other system, spanning almost all console generations except the first. I'd recommend splitting PC up in different eras like MS-DOS, Windows 9x, Windows XP, Vista & 7 and 8 & 10. This also loosely line ups with the console generations starting with Windows 9x.

 

[Crayon]

Mario
Halo
Parappa

 

[Barry Burton]

Most of these are actually *not* my favorite games on each system, just the ones that came to mind immediately when thinking about each platform.

NES - Super Mario Bros.
Genesis - Sonic the Hedgehog
SNES - Donkey Kong Country
Saturn - Nights into Dreams
Playstation - Final Fantasy VII
N64 - Goldeneye 007
Dreamcast - Crazy Taxi
Playstation 2 - Grand Theft Auto III
Xbox - Halo
GameCube - Super Smash Bros. Melee
Xbox 360 - Gears of War
Playstation 3 - The Last of Us
Wii - Wii Sports
Wii U - Super Mario 3D World
Xbox One - Sunset Overdrive
Playstation 4 - Bloodborne

 

[wreckml]

PS4 should be Uncharted 4 imo. I love Bloodborne, but U4 is a pack-in game with the PS4 right now (like SMB and SMW on your list) and has sold a lot more copies than Bloodborne.