Impossible question, let me try:

1st: Pong (because that's pretty much all there was, and it's probably the most important game ever anyway)
2nd: Pac-Man (tough choice, but I think Pac-Mac's legacy beats Space Invader's, was also the first really huge hype)
3rd: Super Mario Bros. (indisputable, the game that saved industry, we should all thank it on our knees)
4th: Sonic the Hedgehog (the game that made gaming "cool")
5th: Super Mario 64 (set new levels of interaction in a 3D environment, gaming wouldn't have been the same)
6th: Grand Theft Auto III (raised the standard of open world and scale, everything followed it's example)
7th: Wii Sports (like it or not, this game opened up new doors for the industry like none before)
8th: as of now still undecided

Some of those were pretty hard to pinpoint. I already mentioned the second gen, but the fourth gen is where things got spread out in all directions it tough to select one that really had the biggest impact. Then there's the 5th gen, was thinking Ocarina of Time, but I guess it's really just a refinement of Mario 64. I've also ignored mobile only games, Pokemon and Tetris would have been good contenders otherwise. Also funny that most are nowhere near my favorites of games. In fact, only Super Mario 64 is one of my favorites, though I do also very much enjoy a good game of Pong (or it's hundred variations), there's something attractive about the simplicity.

The first generation was practically just Pong anyways and I think the only one which can be said to be objectively the game of it's generation.

Second I would give to Space Invaders, Donkey Kong, Pac-Man and Combat. All of these games are either arcade games or based on previous arcade games. Combat mostly just symbolizes the Atari 2600 and what it stood for as a console.

Third goes to Super Mario Bros., The Legend of Zelda, Tetris and Castlevania. All four deserves a mention for being genre setters and influencing the entire industry as a whole, even to this day.

Fourth to Sonic the Hedgehog, Street Fighter II, Super Metroid, Doom and Pokemon Red/Blue. I think for the most part these are fairly obvious, Super Metroid was not the first game of it's kind but it set the standard for Metroidvanias and speedrunning.

Fifth for Super Mario 64, The Legend of Zelda: Ocarina of Time, Metal Gear Solid, Warcraft 2, Final Fantasy VII. Warcraft 2 helped to put Blizzard on the map along with paving the way for future RTS games and MGS paved the way for narrative based games.

Sixth for Grand Theft Auto III, Halo 2, World of Warcraft, Resident Evil 4, and The Elder Scrolls III Morrowind. All of these games redefined, expanded or created new genres. Halo 2 I think is the step between older console FPSes such as Goldeneye and newer ones like CoD 4.

Seventh for Uncharted 2, Wii Sports, Nintendogs, LoL/Dota 2. U2 really set the bar for cinematic games, Wii Sports and Nintendogs attracted a lot of new gamers to the scene. LoL/Dota 2 are pretty huge eSports games and have grown to be pretty massive.

We have yet to see if VR will take off though.

Just about. CoD4 inspired a plethora of online multiplayer games after it.

Indeed but did it have a lengthy history in 2d gaming like Mario did at the time of SM64? Again, the industry was transitioning to 3d at the time and there's just something so symbolic that a franchise once so married to 2d was able to pull off 3d so well. Almost felt like it was setting the example for other 2d franchises to follow suit.

You crazy.

Oh ok sorry about dat.

Those are all console games actually.

Sorry, indeed they are. Your listing of Elder Scrolls games just made me lament the fact that I'm too ignorant to be able to incorporate any PC games into my list...

No need to apologize.

2nd Gen: Pitfall!
3rd Gen: Mega Man 2
4th Gen: Super Ghouls 'n Ghosts
5th Gen: Donkey Kong 64
6th Gen: Eternal Darkness
7th Gen: Dark Souls II
8th Gen so far: Bloodborne

SNES Gen:

PS1 Gen:

PS2 Gen:

PS3 Gen:

PS4 Gen (so far):