First Person Shooter: Half Life (PC). Multiplayer: a tie between Goldeneye (N64) and Team Fortress Classic (PC).
Good old platform: Super Mario World (SNES), Prince of Persia (SNES), Super Contra (SNES), Yo Noid (NES), Super Mario 3 (NES)...
RPG: Final Fantasy VI (SNES), Final Fantasy IX (PS2)
Adventure: Grim Fandango (PC). Also: Monkey Island 1 2 & 3, The Dig, Day of the Tentacle (all PC).
3D Action: Metal Gear Solid (PC version), Metal Gear Solid 2 (PS2), GTA Vice City (PS2)
Sim games: SimCity 4, The Sims 2, Theme Hospital, Theme Park, Mundo (the game I'm developing on my free time)
Strategy: Age of Empires 2 (PC)
Fighting games: Capcom vs SNK 2 (PS2)
Good Star Wars games: Rogue Squadron, Tie Fighters, X-Wing vs Tie Fighters, and yes, even Yoda Stories