Here's how you can download the Titanium Backup app free for Android devices.
1. Go to the Google Play page for the free app Titanium Backup.
2. Tap the Install button.
Here's a description of Titanium Backup:
"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."