Hey, I experienced this problem as well. I am running a Windows 7 PC with the latest version of iTunes (as of 1/5/14) and an iPod Touch 3rd Generation. I tried the .exe modification in the Run window (this supposed fix is found on several sites), and it didn't work. With such an old iPod, it seems as if the new version of iTunes is actually unable to back up the device (imagine a 16 hour backup attempt with no progress). The only reason I wanted to hook my iPod up to iTunes was to sync all my music on my computer with my iPod.
I have also included a picture at the bottom of this post with steps.
-Here are the steps I took to get around the hassle of backup:
1. I just restored the iPod. I didn't care about what I already had on it.
2. In iTunes, I went to Edit:Preferences:Devices then chose to "Prevent iPods, iPhones, and iPads from syncing automatically". This will disable automatic backup and sync attempts when you plug in your device.
3. Now, to sync my music, I plug in my iPod, select it, then go to Settings on the left, and select Music.
4. I then check or uncheck the boxes saying 'Include music videos' and 'Include voice memos'. I have none of these.
5. After this action is performed, the option to 'Apply' will appear in the lower right hand corner of iTunes, which will apply the changed settings to the device, along with syncing all available music and album artwork, etc.
6. The time it takes to sync will vary, depending mainly on the amount of syncable music, but it takes me approximately 1 minute to sync another album I got.
Hope this fix works for anyone searching for one!