In my humble opinion:
Singleplayer FPS: Wolfenstein 3D, because eventhough it wasn't first, it popularized the genre.
Multiplayer FPS: Quake 1. It turned multiplayer gaming into something that everyone was doing. Seriously, there weren't any Doom tournaments or clans as far as I'm aware.
Turn-based Strategy: Civ 1. 'nuff said.
Survival-horror FPS: System shock 1. The format of that game is pretty much kept intact even today, minus all the garbage.
Beat-em-up: Street Fighter 2. Is there any contest over this?
Space sim: Elite. It defined the genre, and introduced the concept of space trading that became so popular.
RPG (Diablo is NOT an RPG!): Ultima IV. It was the game that introduced the actual concept of playing a character. You didn't win by hacking your way through the world; you won by establishing a moral precedent.
FPS RPG: Ultima Underworld. Seriously, it was basically Daggerfall or Morrowind - but released ten years earlier.
Isometric action: Diablo. 'nuff said. Though Nethack or Rogue could be said to have influenced Diablo a lot, Diablo made it all real-time.
Racing: Need for Speed. It was revolutionary at the time.
Adventure: Hard to say, but probably Zork, through its puzzle-solving architecture and vast popularity.
RTS: Dune 2 for basic structure, C&C for setting, interface and strategy design. Starcraft gets an honorable mention for influencing a whole line of hybrid RTS/Squad RTT games.
MMORPG: Lords. It created the entire MUD genre (which is still huge), and by extension defined the basic formula for every MMORPG ever since.