Here's the most trusted and powerful app, called "Titanium Backup". Voted #1 TOP ROOT APP on Twitter.
Install at Google play. PRO Key is available on Play Store!(but you'll get APK for free here)
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Require : ROOT, Android 1.5+
Size : 5.89 MB (apk)
Installed : 10,000,000 - 50,000,000
Titanium Backup is the most powerful backup tool on Android.
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.
Free download with adf.ly link
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Scroll down for more info, Screenshots and DEMO VIDEOS.
What's New
• Can specify power conditions on scheduled jobs.
• Added initial support for Android 4.3.
• Added data exclusion for Media Storage (ie: gallery cache) (enabled by default).
• Fixed "convert to system app" issue on Android 4.2+ (some converted apps failed to work).
• Fixed issue with XML call log restore: the names weren't getting restored on some platforms (eg: HTC One).
• Fixed Android 1.5 support (was broken in TB 6.0.5.1).
• Updated translations.
In this Pro 6.0.5.1 Patched version, you will get;
[✔] 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!
Originally from Google Play Store.
Screenshots;
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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
Here's the older TB demo video:
http://youtube.com/watch?v=pZdqITHxCsM&hd=1