Don't Look Back is a very brief, very challenging game made by Terry Cavanagh, who is better known for popular titles Super Hexagon and VVVVVV. The game is free on the App Store, and it can be beaten in a lunch break. It also happens to be one of the most thought-provoking experiences you can have on your iPhone or iPad.
The game starts out with you, a nameless, faceless character standing before a grave. Nothing about the story is explained for the entirety of the game, but you're immediately able to move forward and explore. You soon find a gun, as well as a variety of fast-moving enemies. You'll shoot the various living threats -- which include snakes, bats, and spiders -- and avoid traps to survive as you push forward for seemingly no reason.
The entire adventure is so short that I really don't want to spoil the mid-game twist for you, but suffice it to say that the reason for the game's name becomes immediately apparent once you've crossed the halfway point. The game ends sooner than you expect, which ends up leaving you with more questions than answers, and you're left to draw your own conclusions about who you are, and who it was that lies below that mysterious gravestone.
Don't Look Back has been available on the App Store for over a year, but it's never really received the recognition that it deserves. It's totally free, there's no in-app purchases, no achievements, and only the hollow shell of a plot, but it remains one of finest examples of experimental game design on the App Store. Play it.