My favorite games are Castlevania, God of War I, II, and III (I just wish they were on Xbox 360 and not PS2/PS3) and The Sims games. I'm saving up now for Assassin's Creed: Revelations and I'm hoping it will be as good as the trailers have made it out to be.
Right now I'm loving Skyrim (I can't even begin to tell you how many hours I've logged playing that game!), L.A. Noire, Red Dead Redemption, and Grand Theft Auto: IV.
There are too many games I like to name a single favorite, but my favorite genres are probably Action/Adventure, RPG, and Simulation. I don't spend a whole lot of time playing Shooters, but I will play them some, especially on Xbox Live.