By genre, my picks are as thus:
FPS
Wolfenstein 3D- Pioneered the genre
Doom- popularized it
Goldeneye- made it possible for consoles
Half Life- Introduced decent plots
Unreal Tournament- Made online play what it is today.
Halo- perfected and popularised console shooters. Intergrated vehicular combat seemlessly
Half Life 2- Perfected physics
Far Cry- not just pretty, but gave an air of freedom and non-linearity which can be seen in many shooters today, and is seriously underrated.
F.E.A.R- to my mind, boasts the finest AI in any game atm.
Action Adventure
Super Mario Bros- popularised and perfected the 2d Platformer
Sonic the Hedgehog- gave hope to other developers that it was possible to compete with Mario
Super Mario 64- added a dimension seemlessly
Grand Theft Auto III- not the first 3d sandbox game (Rockstars earlier work Body Harvest can be thanked for that, and provided the basis for GTA III's sandbox) but the one that made the genre what it is.
Fahrenheit- love them or loathe them, this gave birth to quicktime events.
Metal Gear- pioneered stealth (later Metal gear Solid games could be said to merely be more complex versions of this predecessor)
Max Payne- brought us the best bullet time feature, possibly only contended by FEAR on PC
Tomb Raider- Released around the same time as Super Mario 64, this did many things for many genres.
Racing
Sega Rally Championship- before this game, 3D racing was a joke. Introduced drifting and manual transmission
Moto GP: URT- finally changed the running joke that was motorcycle sims.
Mario Kart- followed by many clones, this pioneered racing for those who didn't give two flying fucks about ground clearance, or even know what that meant.
Gran Turismo- was for those who did no what ground clearance was.
Fighting
Street Fighter II- for obvious reasons. (I would include MK, but that and this just go hand in hand)
Soul Calibur- sped things up, and was possibly one of the most tactile and complex fighting games, which is yet to be surpassed by its sequels.
Dead or Alive 2- Introduced multi-tiered arenas and a perfected counter system (and tits! *sigh*)