If you get the message "Backup not successful", I had the same problem.
My solution was to turn off some apps (Settings>iCloud>Storage & Backup>manage Storage, tap my device name in the Backups section, then look under Backup options) and try a manual backup. If it didn't work, turn off a few more apps and try a backup. Keep doing that until the backup works. Then try adding in some of the last batch of apps that were previously turned off - the objective is to find the app that causes the backup to fail. For me, I suspect that the one app I found had a bad data file that, when included in the backup, caused the backup to quit.
This can be a long process if you have a lot of apps that you originally turned on for backups.