Some of the Xbox 360s have been known to have issues with their DVD-ROM Drives, On Older Xbox 360s The actual Drive has been known to cause slight scratching and scuffing to your Games.
If your Xbox 360 is having problems reading games, their is potentially a problem with the DVD Drives Laser, i had this issue last year with mine, Out of the blue the DVD Drive stopped working and wouldnt read discs. The i would suggest Calling Up the Xbox Customer support Center for your Country (numbers Available on www.xbox.com/support
) and explain your problem to the person on the end of the line.
The only solution is usually to return your Xbox to microsoft Free of charge, which will be either repaired/replaced and sent back to you.
Also, once the solution is solved, it is important to NOT leave Games/DVD's In the Xbox's drive when not in use, Especially when moving the Xbox around as this can knock the laser and cause a fault ! their is only ever a DVD in my xbox drive when it is in use, i take mine out all the time to help prevent these sorts of problems.
Hope This helps !?