Day 2 - This question is really broad. There are too many genres for me to pick an end-all favorite. So....I'll list my favorites per genre I can think of!
Favorite 2D Platformer:
Sonic 3 and Knuckles
Favorite 3D Platformer:
Banjo Kazooie
Favorite Hack N Slash:
Devil May Cry 3: Special Edition
Favorite Survival Horror (and third person shooter):
Resident Evil 4
Favorite Fighting Game:
Mortal Kombat 9
Favorite Party Game:
Super Smash Bros Melee if it counts. If not, Mario Party 2.
Favorite Racing Game:
Mario Kart Double Dash
Favorite RPG:
Xenogears, Mass Effect 2, Kingdom Hearts, or Tales of Symphonia. All too different to choose just one. D:
Favorite Adventure/Visual Novel Game:
Phoenix Wright: Ace Attorney
Favorite Action/Adventure:
Legend of Zelda: Ocarina of Time.
Favorite FPS:
Goldeneye 007 (not too into this genre, but I had good times with that game).
Favorite Puzzle Game:
Shadow of the Colossus (totally a puzzle game disguised as an action/adventure).
Favorite Sandbox Game:
Grand Theft Auto 4 or Fallout 3
Favorite Stealth (or part stealth) Game:
Metal Gear Solid or Batman Arkham Asylum
Annnnd, I can't think of anymore. Out of these, the one that's had the most impact on me, and I've played the most, is probably Sonic 3 and Knuckles, so I could have probably just listed that and shut the hell up. But too bad!