Those of us with 360's are are currently playing a lot of Burnout: Paradise, If you want to join us you can download it directly for $20 from the XBL marketplace.
Or if your cheap you can get it off amazon for as low as $5 off amazon. (<-link)
If you're bored of your current 360 games and are looking for something new it's a pretty good game, and you can't beat the price (used copy for $5). It's pretty much like grand theft auto, meaning its a open world. A player can invite you to "freeburn mode" which is pretty much a open world that up to 8 people can drive around and play a shit load (over 500) minigames/challenges/game modes etc. Or you can just drive around, doing stunts, and taking down random players. (aka banditing as me and Mini call it.)