For my first review, I'm going to recommend a game called 100 Floors, available for both Android devices and iOS.
100 Floors is a puzzle game, where the object of each floor is to solve the puzzle that opens the door to the next level. As the name suggests, there are 100 floors to pass in order to beat the game.
The game starts off with a few "tutorial" levels which give clues as to how the game play works. Almost any aspect of manipulating your phone (or iPod Touch) can be used in this game, from poking, pinching, shaking, to adjusting the volume. Some levels could involve pressing buttons, moving and manipulating objects, deciphering clues, and any other variety of puzzle you can come up with.
As the game play continues, the puzzles get increasingly more difficult, but in my experience I've found the difficulty can very much just rely on how you think. Some floors I've passed in seconds frustrate my friends for a long time before figuring it out, or requesting a hint from me.
I've found the game to be extremely enjoyable, and am currently two floors away from beating all 100 levels. However, at times I've found the game can be super glitchy. Solutions may require super accurate actions that can be difficult to pull off, making it possible to attempt the correct solution without actually opening the door and beating the level. Other floors are just annoyingly difficult to pull off, but overall the game is very well-balanced and has plenty of different puzzles to work through, giving something for every type of puzzle-lover.
Fitting the perfect balance of frustrating and rewarding, 100 Floors is a great game to download and play when you want a distraction which works your brain.