There's something refreshing and low-stress about playing a mobile game without in-app purchases. Knowing that you're spending a couple of dollars to get an entire game that you can actually finish from beginning to end without being hounded to buy coins or gems or some other sort of in-app currency really makes the experience better.
(If you don't mind some in-app purchases, you should check out our roundup of the best Android games of the year!)
Added Downwell, Reigns and The Room series to the list!
The Room series
Grand Theft Auto
Dumb Ways to Die
Freja and the Sequel
Five Nights at Freddy's 4
Grab your gun boots and jump down the well in Downwell. This retro-styled roguelike game is extremely challenging, featuring a pretty steep learning curve as you learn how to defeat the enemies and figure out which weapon upgrades work best for your play style (Hint: it's the Noppy).
Since your character is falling, enemies and shops come from the bottom-up, so you need to be strategic in your freefall do you don't accidentally land on an enemy and lose a heart. There are a number of different 'styles' you unlock through repeated play, which give you different numbers of hearts at the start, changes the way end of level upgrades work, and slightly alters the way your sprite falls down the well.
The goal is to survive as you fall deeper and deeper down the well. There's no in-app purchases, save points, or continues, so when you die you must start at the entrance of the well again.