Very little, most of them will need a PC at least. Reason being Android devices do not let users access data in the data partition where app data is installed and written to. Then there are application who stores data else where rather than the standard directory but accessible to the user vie file managers.
You can try Samsung's smart switch to backup into an external SD card.
IT will not save your app data but only keep the apk stored in a backup so when you restore it can help you reinstall the application. That way you do not need a PC and can just use the external SD card.
Otherwise, Helium is the best option I heard so far... But there are some catch.
https://play.google.com/store/apps/details?id=com.koushikdutta.backup
Helium will NOT backup photos or videos
Helium will NOT backup system files, widgets or voicemail (visual or otherwise), nor will it backup device specific apps like s-note or s-memo. It will not backup your contacts, those should be backed up to your gmail account
Helium will NOT backup MMS messages, only SMS
If you're using a non-root device, you MUST connect to a PC via the USB port of your device to enable ADB backup permissions. HAVING THE PREMIUM KEY WILL NOT REMOVE THIS REQUIREMENT. This will be necessary at every reboot of the device.
Problematic applications to backup (errors during backup/restore)
All Google apps.
Injustice: Gods Among Us
Entire Plants V. Zombies Franchise
Need for Speed Franchise
Candy Crush
Simpsons Tapped Out
Furby Boom
Smurf Village
Asphalt series
Later FIFA games
Temple Run Franchise
Need for Speed Franchise
Good luck, Android never had a good back up process as it is not enforced and too diverse.