I can recommend you the greatest smartphone game ever (this is the second game and it came out a few days ago):

https://play.google.com/store/apps/details?id=laubak.android.game.bad.roads.two.donate&hl=tr

The first game was also great. If you don't wanna pay money there is an ad-supported free version as well. I pretty much only play this game on phones, tried a lot but touch screen controls just doesn't work for me.

- Real Racing 3
- Dead Space (that is pretty much the best mobile version of a famous franchise)
- Dead Trigger (the first one. The second is a festival of in-app purchases and always online DRM)
- Need for Speed Most Wanted (pretty good racing game)
- Triple Town (puzzle)
- Dredd
- Sonic 4 (all episodes)
- Shadowgun (there are two games, the single player one that's is paid and a spinoff, Shadowgun Deadzone, with multiplayer combat, that's pretty good too).

Dead Trigger, Sonic and Shadowgun Deadzone supports controllers (I tested only those, with a DS3 using a USB OTG cable)..

https://play.google.com/store/apps/details?id=com.codestalkers.rogue

I don´t get the low rating. Game is awesome.

I didn't download the game but from the looks of it, it requires a fairly high-end phone (or at least mid-range) to work well. There are always some people who have a 100$ phone and expects every game to run at 60 fps. Most of the time those 1 star ratings come from those. 4-stars review is not really a low rating anyway.

There are more Android games out there than you can possibly take, but quality might be scarce compared to the App Store. I would recommend you check 1) Ninja Barbecue Party, 2) Candy Crush Saga, 3) Papa Pear Saga, 4) Modern Combat 4, 5) Deus Ex: The Fall, 6) Subway Surfers, 7) The Amazing Spider-Man and 8) Numbs, a forthcoming coming numbers game to watch out for. Happy gaming!