Some of my favorite apps are:
Games:
Retroarch (Free emulator, emulates NES - PS1, + extras.)
Mupen64 (Free N64 emulator, ad-free version free on authors website)
Super Hexagon (Paid, extremely hard 1-minute style game)
Solar 2 (Paid, simulation of a space object, from asteroid to black hole.)
Sonic CD (Paid, excellent port of Sonic CD)
Other:
Papyrus (Free/Paid, take notes with a stylus)
Write (Paid, tablet only, take notes with a keyboard)
ES File Explorer (Free, best file explorer out there AFAIK)