On the iPod Itself
Depending upon what type of iPod you have, the serial number is either engraved on the back case, or is on or below the clip.
Where is the serial number on an iPod Touch? On both the regular iPod and the iPod Touch, it is engraved on the back case towards the bottom.
On the iPod Nano (6th generation), it can be found on the inside clip edge touching the back of the device. For earlier models, it is engraved on the back case towards the bottom of the iPod.
On the iPod Shuffle (2nd generation), the serial is engraved on the inside edge of the clip on the back of the iPod. You have to open the clip to find it.
For other iPod Shuffles, you can find the serial number on the back of the iPod (the side with the Apple logo) on the bottom right side.
When reading the serial number on the back of the iPod, the letters and numbers are very small and can be hard to read for some people. You can use a magnifying glass if you need to.