Rockband + Guitar Hero III: Great for hanging out with friends or on your own time.
Seconding Bioshock and Assassin’s Creed. Bioshock is a blast and it’s really intense; Assassin’s Creed is fun playing the story or just messing around.
Normally I’d say Res. Evil 4, but it’s just not the same any more since I played it for the Wii. Actually pointing and shooting is just so much more fun when it comes to zombies.
One that hasn’t been mentioned, but I found it to be a lot of fun is Dead Rising. It is a zombie where you kill lots and lots of zombies. It has RPG sort of stats and is pretty fun. The story is also pretty neat. It is older so you should be able to find it pretty cheap.
I remember a fuss around Dead Rising, I might think about it.
For some reason my 360 has decided not to see my Lost Odyssey disc 3 (right near the end of it too), nor my friend’s disc 3, so I’m gonna return it this Saturday and get it swapped for a new one (the console, not the game)…
That’s really too bad 
Disc 3 was really the highlight of the main quest in Lost Odyssey.
For fighters you should get Dead or Alive 4 and Soul Calibur. For shooters get Halo 3 and the Condemned series. And for RPGs you should get Eternal Sonata. There is a lot of good games out there… Just look around the stores. Devil May Cry is badass as hell so that is a definite pick up. Also get Dead Rising, it’s the best zombie game out there right now.