Here are some:
# Amped 3 (2K Games)
# Call of Duty 2 (Activision)
# Condemned (Sega)
# Dead Or Alive 4 (Tecmo)
# Elder Scrolls IV: Oblivion (Bethesda)
# Final Fantasy XI (Microsoft)
# Full Auto (Sega)
# Ghost Recon: Advanced Warfighter (Ubisoft)
# Gun (Activision)
# Kameo: Elements of Power (Microsoft)
# Madden NFL 06 (EA)
# NBA 2K6 (2K Games)
# NHL 2K6 (2K Games)
# The Outfit (THQ)
# Perfect Dark LE (Microsoft)
# Project Gotham Racing 3 (Microsoft)
# Quake 4 (Activision)
# Ridge Racer 6 (Namco)
# Saints Row (THQ)
# Tony Hawk's American Wasteland (Activision)
# Top Spin 2 (2K Games)

Which ones do you recommend?
I played Kameo and saw Kong, but I also played Call of Duty 2, which was c001. Call of Duty 2 is most recommended by me.

You know what? I think this list is outdated...
I know for a fact that Oblivion isn't coming until 2006.

Out of those games...Ghost Recon.
All of the Tom Clancy games are good. If you like FPS, it's the way to go. I'm positive there will be Online Play. Ghost Recon 2 was a big hit, and is also very fun...especially online.

If you like RPGs...Elder Scrolls IV: Oblivion.
Morrowind was a great game. A groundbreaking game for Xbox, and wildly successful. Not to mention fun because of it's free-form, non-linear gameplay. I'm sure Oblivion will be just as good.

Have you played these games?

i reccomend Call of duty 2
its grand

Call of Duty is also a big pic. I'm sure that any FPS will be great on the 360. CoD, GR, Q4. The Namco Racing series, Ridge Racer will prolly be awesome, as well as the new Burnout. Condemned looks pretty sweet. I have seen gameplay footage for it...this one part, the player holds an enemy with a tazer gun, walks up to him, and smashes his head in with a wooden stick with nail spikes on it! Hw brutal is that?!