I think it's better to ask the question: "What games influenced the general design trends and public perception of it's generation and possibly generations beyond that?" Makes a bit more sense I think. You are more or less talking about the most influential games in history then (at least as far as design choices and public perception go).
NES/Master System
Super Mario Bros. - One of the first games with a true storyline, jump 'n run gameplay in levels spanning much more than one screen, secret areas and collectathons for bonuses, bosses, reflexes and timing went to a whole new level, physics became much more important (running speed, jumping height, impact etc.), more interactive environments (destroyable blocks etc.), upgrades/boosts to find and use (Super Shroom, Starman etc.), multiplayer, each enemy needs a unique strategy to be defeated
The Legend of Zelda - Free exploration of the world, regular expansion of possibilities and accessible areas through upgrades/new items, large and expansive world in 2D, importance of using items/secondary weapons, weak spots for bosses, use of NPC's for support/help, solving puzzles to advance in areas, finding keys to open doors, importance of exploration through maps, save/load system, enemies dropping stuff, money and shop system, gameplay through top-down view
Metroid - Combining the defining gameplay elements from Zelda and Mario into one working formula (2D sidescrolling goodness with free exploration, finding upgrades/new items, weak spots on bosses, finding "keys", and drops on enemies), both horizontal and vertical gameplay, morphing into different forms
Dragon Warrior - Adaption of RPG gameplay to consoles, turn-based battlesystems, using a worldmap as a hub for towns and dungeons, random encounters, big expansion on the level-up and shop systems from Zelda, playing with multiple characters, multi-leveled dungeons
SNES/Genesis
Street Fighter II - Introduction of head-to-head fighters, complex controlsystems and movesets, took blocking and dodging to a new level
Sonic The Hedgehog - Started the mascot craze, gave games a cool edge, open platformlevels with more paths and freedom, emphasized element of speed
Final Fantasy IV - More emphasize on emotional storytelling, maturing of soundtracks
PS1/N64/Saturn
Metal Gear Solid - Made games much more cinematic, took sneaking and AI to a new level, increased interactivity greatly
Super Mario 64 - Showed 3D exploration gameplay could work very well, camerasystem, hub world, multiple goals/level, double/triple jump, new level of physics, true 3D world
Zelda: OoT - Lock-on combatsystem, large and expansive world in 3D, more interactive and physics-based puzzles, night/day element, interactive/puzzle-like bossbattles, quickbuttons for items
Goldeneye 64 - Showed how FPS should play on a console, new level of physics and AI, new control options for FPS, more tactical gameplay, hitzones on enemies
DC/PS2/GCN/Xbox
GTA III - free-roaming and fully interactive world, open-ended gameplay, hybrid of multiple genres, violence gets much more important, gangster themes, very good use of licenced soundtrack, non-lineair mission structure
Devil May Cry - Defined the form 3D actiongames should take, blocking and dodging in 3D, combostrings and hitscores, using RPG elements in 3D actiongames
Halo - Standard for every console-based shooter to follow controlwise, took physics and AI to a new level, vehicular combat, melee attack
Notice how I only focused on games that influenced console gaming. I took PC gaming out of this equation. Also, I could've added games like Gran Turismo, F-Zero, Super Mario Kart and Virtua Fighter, but they only influenced one or two genres specifically. The NES/Master System was clearly the most influential, with the PS1/N64/Saturn generation at second place. To me, these were the two major paradigm shifsts of the games industry on almost every accountable level. The SNES/Genesis generation was a simple improvement over the previous one on most accounts. This is also illustrated by most Nintendo games back then, which simply improved on the concepts set by their predecessors (ie. Super Metroid, Zelda: LttP, SMW). The current generation looks a lot like this, but it seems the next generation simply continues this without bringing any major shift like the so called 8-bit and 32/64-bit generations did. I wonder if Revolution could do something about this.