None FPS huh?
chin tap
Well, you're definitely short changing yourself there, what with the majority of the big name 360 games being some sort of FPS and what not...oh well try these:
Assassin's Creed II
Castle Crashers
GTA IV (and both the expansions, should keep you busy)
Mass Effect 2 (While you may want it for the PC though, it couldn't hurt the pad out your collection on the 360)
Borderlands (Yeah, it's a first person role playing shooter, but it's still good IMHO)
Dead Space (good for an afternoon or two)
These are the games i've played (sans Mass Effect 2, but I've played the first and the second is already ordered) so I can't say much about other suggestions. You might not be a fan of FPS's, but pick up one or two just for kicks. Modern Warfare 2 for instance is a decent choice for some online multiplayer fun, and like I mentioned Borderlands is good, AND it's an RPG with a fuck-ton of loot, and a lot of fun in groups...
Hope that helped...and if not you, hope it helps someone else