How to backup apps and data on non-rooted Android without needing a PC? I know there's ADB backup and Helium and something called Droid Explorer that can help you backup your Android software and data to some extent using a PC, but I want a fully functional non-root, Android-only backup solution (basically, a replacement for Titanium Backup which does it all but requires root). It needs to be able to fully backup and restore apps and data in state. Any ideas?
Such a solution cannot exist without having provisions in the OS itself. The default provision in the OS is the Android backup service   which apps use to backup their data to Google accounts and which adb taps into when a user makes an app backup request. Any solution outside of tapping into backup service would require breaking apart the security model of Android and tap into the private data of apps. Naturally, such a solution is not going to be available without root access.

So your choices come down to these two:


use a PC with a software using adb in the background for app backups, or, use an app which requires adb running in wireless mode (such as what Helium requires; adb wireless needs to be started using PC though) so that the app can use adb to backup apps without further needing a PC.
root the device and do whatever you want with any app and its data without needing the PC.