Best First Person Shooter - *shrug* Goldeneye?
Best Role Playing Game - Chrono Trigger/FFV/FFVI
Best Online Game - Maple Story
Best Real Time Strategy Game - Ogre Battle
Best Fighting Game - Super Smash Brothers Melee
Best Racing Game - Mario Kart... 64.
Best Flying Game - Em.. I dunno. Diddy Kong Racing?
Best Puzzle Game - Oh my. Tetris Attack or Meteos.
Best Simulation Game - Simcity 3000
Best Strategy Game - Advance Wars: Dual Strike
Best Tactics Game - Final Fantasy Tactics Advance/Tactics Ogre: The Knight of Lodis
Best Action/Adventure Game - Jet Force Gemini
Best Platform Game - There's lots. Eh.. Super Mario World.
Best Game Boy Advance Game - FFTA/Fire Emblem:TSS/Pokemon Ruby/Wario Ware:Twisted/Mega Man Battle Network 2/MMBN3/Minish Cap/Tactics Ogre ( )
Best PSP Game - Even though I've never played it, Lumines.
Best DS Game - Advance Wars: Dual Strike
Best Gamecube Game - Metroid Prime
Best Playstation 1 Game - One of the FFs.
Best Nintendo 64 Game - Jet Force Gemini
Best Gameboy/Gameboy Color Game - Pokemon Gold/Silver
Best SNES Game - Chrono Trigger/FFV/FFVI
Best NES Game - Punch-Out!/FFIII
Best/Most Original Game - Jet Force Gemini.

Edit: No DS Love?