I'll contribute! It's an old topic, but worthy of being bumped, since I am heavily into XBox 360 (I have nothing else!) lately.
- Gears of War
- Elder Scrolls IV: Oblivion
- PGR3
- Ghost Recon: Advanced Warfighter
- Guitar Hero II
- F.E.A.R. (If you've played the PC version, don't bother, it's practically the same.)
- Rainbow Six Vegas
- Lego Star Wars II (surprisingly pretty awesome, and only cost me $20)
- Doom (if you've never played the original Doom, it's only $10 on the arcade, complete with 4 player multiplayer where you can actually find games, or play co-op!)
Games that disappointed me, but are still worth renting/downloading the demo and buying if you're into it:
- Prey
- Perfect Dark Zero
- Shadowrun
I am also told that Call of Duty 3 / The Darkness are good games, but I haven't tried either. You can take my brother's word for it or not.
There are a few good classics on the arcade that are only 800 points ($10) as well. i.e. Bomberman, Castlevania, Doom, Gauntlet.
The best part about the large majority of these games is: you can download their respective demos for free on the XBox Marketplace! Sure, some are extremely short for demos, but it's only bandwidth and you can delete it right after. Am I right?