Poweramp - the best music player IMO.
Clean Master Lite - cleaning junk files from your phone with ease.
Greenify - keeping unnecessary apps from running in the background and taking RAM.
Total Commander - very powerful file explorer with lots of functions.
Ampere - app which helps you find out if the charger/cable is getting faulty and not supplying enough power to charge your phone properly.
Caustic 3 - the best beatmaking program on android supporting soundfonts.
Titanium Backup - self explanatory, lets you backup your apps incase something fukks up.Requires root.
Drastic DS - Nintendo DS emulator.
PPSSPP - PSP emulator.