There are two ways that I know of (there may be easier ways, but if there are, I don't know about them).
If you've got a backup of the device in iTunes, then go to the Devices tab in Edit > Preferences and hover your mouse pointer over the name of the device - the serial number should show in a pop-up. You can also find it by going to location of the backup, which should be under :
Depending on how many other iOS devices sync to the computer there may be more than one directory under Backup (one for each device). You can view info.plist via Notepad - search for '<key>Serial Number</key>' which should then be followed by a '<string>' tag which contains the serial number (if you have more than device/directory then first check what comes after '<key>Device Name</key>' to make sure that you looking at the right device).