If you get the error "Backup not successful" and you've tried deleting the last backup and trying to back up manually without luck, try the following test: Go to...
Settings>iCloud>Storage & Backup>manage Storage, tap your device name in the Backups section, then look under Backup options. Turn off all apps from backup and then do a manual backup. If that doesn't work, then this post will not help. If the backup works, then go back to the app list and turn some on and try another backup. If successful, keep repeating these steps. If it fails at some point, then try to zero in on the one app that seems to make the backup fail. (I had this problem and found one app failing, probably due to a corrupt data file.)
This process will take time, but if a backup works with no app data being used but clearly fails with the original settings, then somewhere in the mix of apps is a "bad" one.
Excellent suggestion. Worked perfectly for me too. I lost an iPad2 and replaced it with an iPad4 (can't be bothered with these silly iPad3, 2, 4, yada yada designations). I setup the new iPad4 by restoring the iPad2 content from the backup on iCloud. The new iPad4 works perfectly (except Google Maps and Youtube are missing) but backup to iCloud fails. However, after deleting all the apps from the backup process setup the backup now works perfectly .. and I have begun the slow process of adding more apps (and sill see which app cauxes. the crash of the backup to iCloud.