To be honest, I never really thought about it. Some genres of games I just don't really have an opinion on and/or haven't really played much of. Plus I also go back and forth on which games I consider "favorites", anyway.

I guess some answers I can give are

JRPG: SaGa II
Action Platformer: Mega Man X2
Arcade Shooter: Pocky and Rocky
Rogue-Like: Azure Dreams
Horror: Lobotomy Corp / Yume Nikki
First Person Dungeon Crawler: Artificial Dream in Arcadia

... those last two do sort of feel like cop outs because I haven't played much of those respective genres, but I do like those games.