Game of their respective generation and reasons why

[Leadified]

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.