You realize there aren't too many apps mentioned within this thread? Well, here's a couple for you to start things off... both are games, and are available free from the Google App Store Google Play!
The first is called Cultist, and it takes you back to simpler times, when handheld gaming consisted of beeps, bops, a left and right directional button, and graphics so simple they looked a if there were three to five images, but only one was lit up. Remember those games? Well, this one is just like that, except for your android device! And, the best part is is that it is Cthulhu themed! That's right folks, Cthulhu makes it to the handheld! You play one of Cthulhu's cultists, and you must take a sacrifice and place her on the alter for Cthulhu to devour, but watch out... if Cthulhu's tentacles touch you, you'll be the one devoured! Controls are simple: tap on either the left or right of the screen to move in that direction.
The second game is called Dogfight, where you pilot a World War One bi-plane. Is that even politically correct, a bi-plane? Why not gender neutral? Anyway, you pilot a plane from that era. With your tablet flat / horizontal (docking station removed), the craft is controlled by the tilt of your device... but that's not all! There's a throttle on the right of the screen to adjust speed, a machine gun trigger and a bomb lever as well. There is a tutorial mission where you have to fly through hoops.