XBLA Games:
Penny-Arcade 1+2 if they go on sale. Good adventure/rpg, if you like oldschool (like LucasArts) adventure style
If you enjoy "manager" games, Outpost Kaloki X. Launch 360 arcade game, but a great timed space station builder.
Castle Crashers online is undeniably awesome.
Obviously, the possibilites are massive. This is going to sound flippant, but I'm serious: go to the arcade section of Marketplace, and just hit the demos one after another starting with "A". Even if the games suck, you're out nothing but a half our of playing a free game.
If you really want to stretch the points, check out some of the indie/community stuff. Far harder to find good amidst the crap, but some gems. I'd absolutely get Blow, a puzzle game where you have to arrange wind currents to guide a soap bubble around an environment. Probably close to 100 levels, graphics and music are top notch, multiple game modes, great level design. Great game. Carnivale was pretty neat, and I liked Solar (especially for like 200 points). Again, Demo your ass off.
Actual games:
Echo the Mass Effect and Oblivion if you're into RPGs, and Eternal Sonata. But again, don't overlook the demo back catalogue.
Oh! and Kameo. Great game. To this day I like the cartoony art, great animation, platforming and puzzles, and behind all of that there's the criminally neglected fighting game after the game as well. If you've got a old-Nintendo Mario thing, you might really like it.
**having said all that**
I don't know your game history, but if you haven't been involved with an all-voice chat game network, I really, really recomend you give it a serious try. I'm not talking about teabagging in Halo or annoying crap like that, I mean making a run in Horde mode for Gears or the final Standoff in L4D. Even setting up a Hamburger Hill in GhostRecon. A friendly race or Cat-n-Mouse in Forza (I'd say get 2 but 3's only around the corner . . ).
You've mentioned that the Halo/Gears/Crap games wer'nt of interest, but give them a serious try in the "non-abbrasive" lobbies. Heck, send me a message on XBL (busboy33) and I'll get a group of people to just have some fun blowing stuff up, crashing, or whatever. The effectiveness and transparency of XBL really does make alot of the "not considering" games worth a second look. It sounds stupid, but XBL really can make just playing the game together more important than what game you're playing, and unfortunately most game that excel at group playing involve guns and are usually associated with jackasses.