A surprising amount of 360 games are actually region free, it's mainly EA who are clinging to region-locking.
A mate of mine had a Japanese 360 (he was living in Tokyo during the launch) that recently red-ringed on him, and he ended up having to replace it with a UK 360. Of his 30 or so Japanese games, he had to replace skate. and Burnout Paradise with UK copies, and that was about it.