What do you think? A game can be influential can be other ways besides just play mechanics and graphics, too. Here are my picks.

2600: Space Invaders (first? arcade port)

CV: Donkey Kong (first *good* arcade port)

Intv: Baseball (control scheme)

NES: Super Mario Bros. (introduced platform gaming to the masses)
Genesis: Mortal Kombat (violence in video games)

Game Boy: Tetris (helped sell a ton of Gameboys, introduced gaming to previous non-gamers)

SNES: Super Mario Kart (arguably the best multiplayer racing game at that point)

N64: Mario 64 (3d platforming)

Dreamcast: Soul Calubur (first home fighting game that was as good as an arcade one)

Feel free to disagree, and add the systems I left off.