I tried another user account (adding my iTunes Library from an external hard drive) and the same thing happened. I then added my music library to my MacBook Pro and connected my iPod.
Worked perfectly.
Therefore, it's not my iPod, or iTunes Library or iTunes itself. It's my iMac. I did a fresh install of OS X a few days ago, and this may have caused a problem. So I'm going to install OS X again later this evening and that should solve the issue. I'll post back with the result.