On your iPod packaging
If you still have the original packaging for your iPod, you can find your serial number on the barcode label that is affixed to the packaging.
On your iPod invoice or receipt
Some retailers may include the serial number of your iPod on the receipt.
Online at My Support Profile
If you used your Apple ID to register or purchase your iPod, you may find the serial number listed in My Support Profile (available in the United States and Canada). Log in with your Apple ID and find your iPod in the "My Products" box on the main page.