New 360 and I need game recommendations

I finally bought a 360 this week (with the $50 TRU giftcard offer, so I won't feel too bad if the price-cut comes through) Prior to purchase, I've been picking up games that I wanted (including BC), but I want to know if I'm missing any good gems out there for the 360 (not BC).

So far I have for 360: Kameo, Oblivion, Rumble Roses XX, and DoA4 BC=Fable, KotOR1, DoAU, DoA3, Buffy, Morrorwind.

I really don't care for sports games, racers or shooters, although games like Tomb Raider (which I already have on GC) where adventure/puzzle is a much bigger aspect than shooting are ok.

I mainly ask because I don't want to pass up anything I might enjoy, but appear to be having a hard time getting past the "360 only has shooters" mindset.

Check out this thread:

http://www.gamespot.com/pages/forums/show_msgs.php?topic_id=24457925#