Titanium Backup ★ root

Titanium Backup is the most powerful backup tool on Android, and then some.

You can backup, restore, freeze (with Pro) your apps + data + Market links. This includes all protected apps & system apps, plus external data on your SD card. You can do 0-click batch & scheduled backups. Backups will operate without closing any apps (with Pro). You can move any app (or app data) to/from the SD card. You can browse any app's data and even query the Market to see detailed information about the app.

Also see the paid PRO key which adds EVEN MORE awesome features such as:
[✔] 0-click batch restores
[✔] Keep multiple backups per app
[✔] Backup/restore SMS,MMS,calls,bookmarks,Wi-Fi AP as XML
[✔] Multi-user app data
[✔] Apps freezer
[✔] Sync to/from Dropbox (manual/scheduled)
[✔] Sync to/from Box (manual/scheduled)
[✔] Sync to/from Google Drive (manual/scheduled)
[✔] TB Web Server: download/upload your backups as a single ZIP on your computer
[✔] Convert user apps <=> system apps
[✔] Integrate system app updates into ROM
[✔] Encryption
[✔] Market Doctor (relink apps to Market)
[✔] "Destroy all Market links" feature
[✔] Hypershell speed
[✔] Backup apps without closing them!
[✔] Create your own update.zip containing apps+data!
[✔] Restore individual apps+data from non-root ADB backups!
[✔] Restore individual apps+data from CWM backups!
[✔] Restore individual apps+data from TWRP backups!
[✔] Market "auto updating" manager
[✔] Dalvik cache cleaner
[✔] Integrate Dalvik cache system elements into ROM
[✔] Unlimited schedules
[✔] Load/Save a Filter and use it in Widgets/Schedules
[✔] Change the device's Android ID, restore it from a backup or after a factory reset
[✔] Protect backup against deletion
[✔] Send backup (to e-mail/cloud) and import it in 1 click
[✔] Backup→Verify→Un-install an app in one shot
[✔] Freeze/defrost/launch apps in a single click
[✔] CSV export any app DB (e-mail or Google Docs)
[✔] Convert app data to/from fast WAL format
[✔] WAY MORE!

Check out this in-depth review of TB PRO:
http://youtube.com/watch?v=vuvDTS9RDrM&hd=1

And check out the new TB PRO demo video:
http://youtube.com/watch?v=YU33zabluSY&hd=1

More info on permissions:
• "Internet" is used to access Market,Dropbox,ChangeLog.
• "Accounts" is used to access Market.

Some advice:
• We recommend to avoid "modified" TB versions because they can cause various problems down the road.