If you have $15 to spare and a love of serious RPG's, Square Enix has your number. Drakerider has just arrived in Google Play, and this isn't a port of a console game. It's a new experience designed specifically for touchscreens.
In Drakerider you ride around on a dragon completing tasks and doing battle. The fighting system is a little different than most RPGs. You keep control of your dragon mount with the reins when you need more control, but ease up to allow it to attack enemies.