Can't sync iphone with Mac after restoring from TimeMachine
After spending almost the entire day on this problem, I found the solution: I had to thoroughly re-install iTunes, using FineWine's step-by-step guide.

Here are the things I did before that, but which had no effect:
- Tweaking every possible setting in iTunes
- tweaking every possible setting on my iPhone
- reinstalling the latest backup
- reinstalling the backup from last month
- reinstalling the backup from a year ago
- deleting files on my phone manually
- doing several iPhone hard resets
- upgrading to iOS 6 (!)
- and more