It was giving me 2 errors: 'Couldn't retrieve profile from Sync Services -- unplug and replug iPhone' and 'Couldn't backup iPhone.' Having restarted, and unplugged/replugged the iPhone, it still wouldn't back up, or even update to iOS 4.3.1. The situation was very vexing.
The issue was available storage space on the iPhone. I had over 700 photos and movies on my 16GB iPhone, which clogged everything up. The solution, of course, was to delete those photos and videos. Having done that, the iPhone finally synched, backed up and updated to 4.3.1.
It may be slightly obvious, but it's good to know that too little disk space on the iPhone can clog up backups.
[crarko adds: Is there documentation about how much scratch space needs to be left on iOS devices for things like updates? A pointer would be handy if somebody could provide it.]

