Well, I'm just going to name out the games that I have picked up and loved to death. So sorry if there are repeats but with the xbox 360 and online play...you can't go wrong with the following games....
1. Halo 3
2. The Orange Box (contains Half Life 2, episode one, episode two, team fortress 2 and portal)
3. Call of Duty 4
4. Mass Effect
5. Rainbow Six : Vegas (number two comes out in 3 weeks. One hellva single player storyline!)
6. RockBand
7. Shadowrun (not for everybody...you love it or hate it. Course it's an online game only!

)
8. Gears of War
9. Condemned: Criminal Origins (oh god, is this game freaky! like Resident Evil on crack! Number 2 comes out later this year!)
10. ChromeHounds (a unique, build your own mech and kill things game. Once again, you like or hate it!)
11. Marvel Ultimate Alliance (get the gold edition!!)
12. Assassin's Creed (another you like or hate title...it does look amazing though!)
13. Dead Rising (one mall, one you. millions of zombies!)
14. Call of Duty 2 (the best world war 2 fps ever!)
15. Crackdown (cops meets heroes!)
16. Earth Defense Force 2017 (game doesn't have fancy graphics or even a good story! But you and a friend go co-op and kill the giant bugs, robots and spaceships, well fighting godzilla like monsters. Blast when you've had some drinks as well!

)
17. F.E.A.R. (your not afraid of the dark are you? or a little girl in a red dress that burns things?

)
18. The Darkness (not bad...good single player game. online sucks though. worth a rental!!)
Anyways there's others like the Dynasty Warriors series but I don't really know your tastes. There are some hidden gems out there that you may like but didn't sell well (area 51 anybody?) So rent and explore!
Oh if you get live...feel free to PM me. I'll ways looking for people to game with!