This one is one you can demo and then pay for the full game, but I highly recommend Reaper: Tale of the Pale Swordsman. The controls and artwork are awesome. And it is so satisfying to chop up those guys. And it's an RPG/ adventure side scroller. Seriously, go buy it.
Besides that one, I would say if you like racing games, Asphalt 8 (or anything made by gameloft for that matter) is good. It runs great, is free (with some in app purchases you can basically ignore or watch some ads to gain currency), and you get extra points and cash for crashing other people's cars.
I'm a tetris junkie at heart so I also say for tetris games to go for Tetris galaxy.
For stupid and simple games (cause we all need those once in a while), I recommend Circle, and for word games, Ruzzle is where it is at.
I hoped this helped, and if you need others, let me know!!
EDIT: here's the link to the Reaper game because that is the one I recommend the most:
https://itunes.apple.com/us/app/reaper-tale-pale-swordsman/id698299228?mt=8