I got this error today while syncing my iPhone 3G with iTunes 9.2 today:
iTunes could not backup the iPhone "iPhone" because the backup session failed.
Re-seating the USB cable and restarting iTunes did not help. A Google search revealed various fixes having to do with firewall settings or 3rd party application conflicts, but none applied to my situation.
Ultimately I solved the issue by running a manual backup of the iPhone by right-clicking (or control-clicking) the iPhone in the Devices section of iTunes and choosing "Back Up." Once that completed I was able to sync without getting the error.
UPDATE: According to the comments on this post, it may help if you first delete the old backup by choosing Preferences –> Devices –> Delete Backup. You should copy your old backup somewhere else before you do this. Your backup is stored in the Users/[username]/Library/Application Support/MobileSync/Backup folder on Mac, or C:\Documents and Settings\[username]\Application Data\Apple Computer\MobileSync\Backup on Windows.
UPDATE 2: According to the comments, Windows users may need to change their computer's time zone to fix this issue.
UPDATE 3: According to the comments, Windows users may also need to kill the AppleMobileBackup.exe process and restart iTunes.
UPDATE 4: According to the comments, Windows users may also need to run iTunes as an administrator. Go to Computer>local disc (c:)>Program Files>iTunes>iTunes.exe then right click and run iTunes.exe as administrator a (iOS 4.0.1 itunes 9.2.15 on Vista)