I believe I just fixed this issue.
Win 7 x64 with iTunes 10.7 and I've been getting the same error.
I did uninstall and reinstall iTunes 10.7 and that DID NOT fix anything.
Right click on the iTunes desktop icon and select Properties and then Compatibility.
Select Run this Program in Compatilibity Mode and Select Windows 7 (I'm assuming this is 32 bit)
At the bottom of the this screen select Run this Program as Administrator.
(Don't know which of these is necessary to check but checking both just backed up my iPhone 4s on IOS6 and the backup is in iTunes.
Please let us know if this works for you.
Further testing has indicated that this is required: Run this Program in Compatilibity Mode and Select Windows 7
Run as Administrator is not required.