No gory? Well that cuts pretty much everything awesome out like Bioshock or Gears of War. Halo 3 is a classic, hands down. a few other good ones are oblivion (if you haven't played it on pc), skate is a nice realistic skate sim, very very different from tony hawk games. spiderman 3 is fun and has a lot of play time in it but a bit repetitive...ummm..... yeah they're my recommendations so far. there are heaps of others, its a sweet console, hardware issues aside.
No gore? Good luck with that.. Halo 3 isn't too gory (and it is no doubt the best game available for now). But honestly, all the good games for 360 are gory! You can try GRAW2 (ghost recon advanced warfighter 2), and other sport or racing games like PGR (project gotham racing) or Madden NFL.
Gears of War and Halo 3 are still musts, even if you don't like gore!