Q: If I have a new, un-synced iPod touch, can I connect to my computer and get iTunes to restore the last backup of my old (stolen) iPod touch to the new one? Both are second-generation iPod touches, running iPhone OS 3.0.
A: Most definitely. By default, iTunes makes a backup of your iPod touch each time you connect it, and when you connect a brand new iPod touch or iPhone to your iTunes library, iTunes will ask you whether or not you want to set it up as a new device or restore it from a previous backup.
Selecting the previous backup will basically set up your new iPod touch with all of the settings from your previous device, including any third-party application data, device preferences, and even your sync settings in iTunes. Your media is not specifically backed up, as this can be synced back from your iTunes library, but your sync preferences such as selected playlists are stored in the backup and restored as part of this process. Basically, after restoring your backup, your new iPod touch should be indistinguishable from your previous one.
Note that if you chose to set your iPod touch up as a new iPod when you connect it, you can still restore the backup manually at any time simply by right-clicking on your iPod touch icon in the iTunes Devices list and choosing the “Restore” option from the context menu.