MS have released a tool to let you migrate game licenses to your new 360 so that games can be played on or off line.
http://www.xbox.com/en-US/support/systemuse/xbox360/licensemigration/
I've just done it and it's pretty painless.
http://www.xbox.com/en-US/support/systemuse/xbox360/licensemigration/
I've just done it and it's pretty painless.