1) What operating system?
2) Connected via USB directly to the computer, not through a hub or anything else?
3) Tried connecting to other USB ports?
4) Got the latest iTunes?
Also, if you have only just got your iPod, you may not have the latest software on it. It may have Firmware 1.1. This should still work fine, but you will not have some of the new functionality of the latest release, particularly the ability to load new applications. A download update to Firmware 2.0 cost �5.99
My itouch has suddenly developed this fault, having worked perfectly since Christmas. People say the Apple Store staff are very helpful - I'll be taking mine to them in the next 7 days so I'll let you know how I get on.