I'll give you some thoughts on my current 360 collection at school, this doesn't include what I have at home
Dead or Alive Xtreme Beach Volleyball (XBOX) - Doesn't play on 360, was a gag purchase. Sits on my shelf and collects dust.
Fable: The Lost Chapters (XBOX) - Haven't really played it much. It runs at a slow choppy framerate on 360 (And maybe on XBOX?) And it really isn't that good. I've heard Fable II is much improved though, it might be worth checking out if there's a demo on the marketplace.
Ninja Gaiden (XBOX) - Yeah, the original. Black is on the marketplace and II is $10 at Best Buy, I hear it applies online. I highly recommend you get a copy of II and if possible 1200 MS poins and Black. The game is hard, but its an amazing DMC-ish beat em up, with ninjas. Nothing is more satisfying than throwing shurikens at the badguys.
Call of Duty 4 - Great online shooter, superb campaign, if you're into FPS at all, I recommend it.
Condemned 2: Bloodshot - Have yet to play this one. Its $10 at Best Buy and I hear its good.
Dead Rising - This game is a masterpiece, and it'll run you $30. You do nothing but chop up zombies in a shopping mall with insane weapons, ranging from squirt guns to MegaMan's buster arm to Fender Strats. If there's one game on the 360 you need to own, this is it. And the Wii port won't be nearly as good, because a lot of this game's magic comes from there being hordes of zombies.
Dynasty Warriors 5: Empires - My roommate buy this for $12 used, and he's the only one that plays it. Repetitive music, lots of button mashing. Think KH but with Chinese and not nearly as fun. I don't recommend this one.
Gears of War 2 - Blood, guts, chainsaws, aliens. What's not to like? If you don't know whether or not you like Gears of War, check out some videos online. Think a fast paced RE4 with enough ammo, and you pretty much have it.
Grand Theft Auto IV - They redid the engine from 3, and it has about the same amount of content as 3. Some people don't like it because it doesn't have all the SA content, but I personally love it. It has online multiplayer where you can just screw around in the city, the competitive multiplayer sucks.
Lego Indiana Jones - Came with 360, haven't played it. I bet you have this one already.
Kung Fu Panda - Same Same
Mass Effect - I haven't played this yet. I hear its KOTOR on roids. Got it for $20 from Best Buy.
Rock Band - Probably the second greatest guitar hero game ever made. I don't need to explain this one. More DLC than GH, four instruments, song difficulty's about the same as of world tour. Its a matter of preference.
Rock Band 2 - The best one, and the sequel to RB.
Rock Band ACDC - $40 at Walmart, not worth the money, BUT ACDC
Sonic Unleashed - Underrated game, when this drops in price pick it up. Sonic stages are fast paced onrails-ish and the Werehog stages are tolerable.
I don't feel like typing anymore, sorry D: