Originally Posted by ExtremeNerd

The only TRUE backup is a NANDroid backup. That can be done in custom recoveries.

If you expect to flash a TON of ROMs, Titanium Backup PRO is the best. It can create a .zip of your apps which you can flash after flashing a new ROM.

For general backup, I would recommend MyBackup PRO. You can schedule a backup (I do it every other night) and forget about it until you need it. It does backup .apk and data if you're rooted. These backups cannot be flashed, but can be restored through the app after flashing a ROM. I also use this for one-off backups of an .apk I want to keep and upload to DropBox.