Best First Person Shooter - GoldenEye
Best Role Playing Game - Final Fantasy VII
Best Online Game - Don't really play online games but the last one I played was Lord of the Rings: The Battle for Middle Earth.
Best Real Time Strategy Game - Command & Conquer Red Alert 2, although the aforementioned comes a close second.
Best Fighting Game - Tekken 5
Best Racing Game - Gran Turismo 2
Best Flying Game - Air Combat
Best Puzzle Game - Minesweeper Flags on MSN
Best Simulation Game - The Sims?
Best Strategy Game - Civilisation
Best Survival Horror - Resident Evil 2
Best Tactics Game - Final Fantasy Tactics Advance (The original isn't out here)
Best Action/Adventure Game - Does GTA: SA count?
Best Platform Game - Spyro the Dragon (One!)
Best Game Boy Advanced Game - FFTA
Best PSP Game - Ridge Racer is the only one I've played.
Best Gamecube Game - Pikmin
Best Xbox Game - Halo I guess
Best Playstation 2 Game - GTA: San Andreas
Best Dreamcast Game - Hahahaha
Best Playstation 1 Game - FFVII
Best Nintendo 64 Game - GoldenEye
Best Saturn Game - See: Dreamcast
Best Gameboy/Gameboy Color Game - Pokemon Red/Blue
Best Super Nintendo Entertainment System Game - FFVI
Best Genesis Game - Sensible Soccer
Best Nintendo Entertainment System - FF
Best/Most Original Game - GTA III. So there.