I really wished I had played more but from the few I played my favorite 5 games of 2016 are:
Star Knight ($0.99) - really fun and challenging hack-and-slash platformer, with a dope art style that reminds me of Limbo.
Pocket Mortys (free) - one of my favorites of the year, created by Adult Swim, it's a Pokemon like game but with Rick and Morty, were you collect Mortys instead of pokemon.
the battle of Polytopia (free) - formerly known as Super Tribes, its my favorite turn base strategy game for mobile so far. The developer recently added multiplayer support as well.
Bullet Force (free) - Multiplayer First-Person Shooter that actually works very well with touchscreen control. Love the game, came out in late November and still addicted to it.
Super Mario Run ($9.99) - An actual official mobile game from Nintendo, a must-buy from me and I actually really recommend it. So far I'm in World 4, collecting all the color coins is very challenging and there's 5 characters to unlock.
Pretty decent games came out in 2016, let's hope 2017 brings us more quality mobile games!