All-Time/RTS = Starcraft. Childhood classic. My first real "hardcore," or whatever term you use, video game. Stays good even after ten years, and the community made maps and gametypes make it feel like more then just one game.
TBS = Fire Emblem: Sacred Stones. Can't pinpoint why I prefer it over the other games or Advanced Wars. I just prefer it.
WRPG = World of Warcraft. Well since I played it for about two years, I guess it has to be my favorite. Played it far more the other RPGs. The first time climb to level 60 was a real adventure, and the raids were amazing group experiences. TBC was good, but the raid content was changed too much and killed the game for me. Forced raids though 10-man Karazhan, and reducing the cap to 25, ruined raids, and the game overall.
JRPG = Tales of Vesperia. Fast-paced and rewarding combat system with great characters, story, and enviornments. Tales of Symphonia had a better overal story, but Vesperia surpasses everything else, including characters.
Puzzle = Portal. You know the drill.
Shooter = Call of Duty 4. The online play is the most addictive I have played.
Action Adventure = Metroid Prime. A great gameplay world. A fluent mix of shooter, puzzles, and adventure elements. Plus a fun arsenal with a large variety of enemies. What is not too like?
Adventure = Neverhood. Another childhood favorite. Fun puzzles with a funny tone too it. I need to find another copy.
Platformer = Sly Cooper: ATTR. Thief and stealth gameplay without any of the boring stuff, plus a stylish cartoon feel, and the coolest racoon ever.
Music = Rock Band 2. OK, so it is really just a $60 track pack for Rock Band with no real upgrades, but importing the Rock Band songs give it the best music game soundtrack, and that is excluding DLC.
Misc. = Trauma Center: Under the Knife. I wish it had more operations based around real health problems rather then a fictional virus, but it was original, fully maximized the DS, addictive, and felt rewarding, even if the patients were fake.