Deep scratches can not be repaired but if you have minor nicks or scratches that cause your games to freeze or not play at all you can try saving them. Since they do not work anyway you have nothing to lose.
The best way to remove minor scratches if with toothpaste. Get a soft cloth and put some toothpaste on it. Start from the center of the disk and go out. Do not go around the disk in circles. Keep working in an outward motion and you will start to see a cleaner looking surface.
Wash the disk well with mild soapy water and dry it completely. It should work a lot better. I have saved a lot of disks with this method. It also works on regular audio cd's and DVD's.
To avoid jamming the DVD drive and damaging discs or the Xbox 360 console:
The best way to Repair an Xbox 360 Game is to make a copy of the original disk and play the copy, That way you can always burn another copy if you damage one. Blank disks are cheap.
See our other post about making backup copies or get Game Copy Pro here.