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Titanium Backup requires root, won't work otherwise.
You could use Helium, which needs to be connected to a PC the first time you use it (or if you reboot the phone) but after that works fine without root access or PC.
Helium can backup app data as well, which means your game saves won't be lost. MyBackupPro requires root to do that. Helium doesn't.
Correct. That's why I suggested it despite the OP saying no PC involvement.
If app data backup is wanted you have to either root and use the backup app of choice or use Helium and a PC startup enabler. There are no other options that I'm aware of.
I can't see the point of backing up apps unless you have some that are no longer available for download, perhaps an old version.
The only part of an app I find worth backing up is the data; the app itself can always be reinstalled from source so there's not a lot of point keeping a local copy of it.
old version or a specific version.2 in case of no longer available. otherwise yes i need a root backpup method for apps data.