Make backups of selected apps on your device and restore from those backups. oandbackup enables you to save app data to a user-accessible location. Both backup / restore of single apps and of multiple apps are supported.
Requires a working busybox installation at the moment (often pre-installed on custom roms).
Requires root: Yes. Copies files from /data/data, /data/app and /system/app.
(If you don't have root but have Android 4+ you can use the command-line program adb from the Android SDK platform tools to make backups via a desktop computer)