Epic RPGs like Morrowind and Oblivion.

I don't have a favorite one. I've played and enjoyed a lot of games. I'll name a few in no particular order:

Action (NMH, Star Wars), Adventure (Zelda, Sword of Mana), RPG (Pokemon, Chrono Trigger, Mario RPG, Skies of Arcadia, Golden Sun), Fighting (SF, SSB, MK), RTS/Strategy (StarCraft, Pikmin, Advanced Wars), Racing (F-Zero, Top Gear, Mario Kart), Simulation (SimCity, Animal Crossing), FPS (CS, MP, Perfect Dark), Platformers in 2D and 3D (SMW, DKC, BK, SMG), MMORPG (Tibia, Maple Story), Shooters 2D and 3D (Gradius, Contra, Star Fox, Descent), 3rd person (RE, SH), Sports (International Super Star Soccer, Wii Sports), Party (Wario Ware Inc., Mario Party, Sonic Shuffle), Puzzle (Minesweeper, Luxor, Bejeweled)

But if I had to choose one, it would be Adventure, because The Legend of Zelda: Ocarina of Time and The Legend of Zelda: A Link to the Past are my favorite games of all times.

Turn Based Rpgs are my favorite, and sports/fighters are my least favorite.

FPS

1. City Building/similar sim games (Sim City, Caesar, Roller Coaster Tycoon, etc.)
2. Strategy (any kind! RTS, 4X, SRPG)
3. RPG
4. 2D Platforming

Adventure and Racing (arcade and kart) are also high on the list.

Least favorite:
Fighting, with the big exception of Smash Bros.

Favorite: Racing, FPS, Platforming, RPG.
Least: Sports.

1. FPS/TPS
2. Strategy/RPG
3. Sports/Racers

least favorites:

platformers,puzzles,party games

Shooters like Gradius, Ikaruga and R-type