Common apps..
Titanium Backup ( Used for backup of apps & associated data on your device. Even system level protected apps with root access )
My Backup Pro ( Same as above, some different options and layout )
Helium Backup ( Works for both rooted and non rooted devices to backup/restore app & data )
ES File Explorer, Root Explorer and various other file management apps ( more extensive features for rooted users, accessing system protected level stuff )
Various ROM & kernel apps by big name and smaller name developers to modifying and customize various things. i.e., Goo Manager, ROM Manager, ROM Toolbox, SetCPU, Xposed app and too many more to name.
There is some of the more common stuff, there is more out there but I think I've hit the main stuff.