We have Project Gotham Racing 3, which is really cool, it's no Gran Turismo but it has really great graphics and it's a lot of fun with a ton of different cars, but no "normal" cars like Gran Turismo has.
We have Madden 07 which is cool but they changed a lot about it since Madden 06 so it depends on if you like the changes.
Battlefield 2 is our favorite game because you can play online and it's just really fun. You can talk to friends and create troops to team up and capture the enemy's flags and the graphics are incredible.
We played NFS Most Wanted on regular xbox so we don't have it for 360.
Saints Row is really fun, we have the demo right now but we're waiting to get some games from my boyfriend's friend in CT because he works at a game store and can get them cheap for us. We're also going to get MLB2k6, waiting on that.
Fight Night, we played the demo and that was pretty cool but neither of us are into it really enough to buy it.
Some other cool demos you should download are the ping pong game, which is surpisingly very fun and there are two different soccer games that are cool.
We got Texas Hold 'Em for free because it was free for the first 2 days but now it's like $10 I think, but it may be worth it even if you don't necessarily play poker because it's fun and addicting.
We also got Street Fighter for like $5. There are a lot of fun cheap old arcade games and yahoo games and stuff.