For fighting style games, try Mortal Kombat DA if you're a fan, or that new Tao Leng (sp?) fighting game made by Microsoft.
Some other fun games I'd suggest:
Splinter Cell or MGS2 (or XIII when it comes out)- great story/action games.
Fuzion Frenzy- There's a demo of this on the halo disc, that's where I first tried it. Very simple minigames and controls, feindishly addictive
Cel damage- pretty fun car combat game although the learning curve is very steep and the ai is really tough on you- that or I just suck at it really bad.
Sadly I have no xbox or xbox games (this summer though....) so I can't sell any to you
Ruahrc