I found a solution that isn't "just nuke everything and reinstall, hoping it doesn't happen again."
This is what I did.
1. Turn off wi-fi sync (this may not be necessary).
2. On the iDevice (mine is an iPad) go Settings - General - iTunes WiFi Sync
3. Sync with USB cable. Watch the status on the iDevice.
4. I discovered that for some bizarre reason, it was trying to install Pages even though it was already installed and running fine with the latest update on my iPad.
5. Delete and reinstall Pages from the iDevice's App Store.
6. Initiate a backup via iTunes on my Mac, including transferring apps/other purchases that aren't on the Mac. (This may not be necessary, but likely is).
That fixed it. The key was to have settings up and running before sync'ing so I could see which app was crashing the sync. Note that the Pages warning message was replaced with the annoyingly unhelpful "preparing for sync" message that iTunes displayed. Also, the iDevice status has more info than iTunes does.