As mentioned in the comments by Firelord and me, there are multiple approaches:
- you could use Titanium Backup
- you could use ES File Manager, which includes an app manager capable of backing up apps and their data
- you could use ADB backup
- You could use Adebar to make the previous step easier
TiBu and ES File Manager require root to work. ADB and Adebar don't.
Adebar a.o. creates a script to backup each of your (user) apps into a separate archive using
adb backup (and another one for the data of system apps, and two others for restore). While you could do a similar thing with TiBu (which uses its own backup format), Adebar runs from the command line while with TiBu you must use a GUI. Side effect from using Adebar: you'll have your device documented: tech specs, apps installed, etc :)
Adebar is pretty easy to install, but will require adb to be available on your computer (see our adb tag-wiki for details on that). It runs fine on Linux, and recently was reported to run on Windows as well via Cygwin.
Disclaimer: I'm the dev of Adebar.