1. Bastion
Not enough can be said about Supergiant Games' Bastion. Thanks to the game's stunning hand-drawn art style, excellent sound track, and unique narration, Bastion holds up as one of the most original, unexpected, and thoughtful games since its release in 2011.
The protagonist, "The Kid," wakes up to find the mysterious Cataclysm destroyed his world and everyone he knew. His adventure—from slaying enemies to falling off a ledge— is narrated by a gravelly voiced man. With a few faithful weapons and a lot of dangerous enemies kicking around, The Kid sets off to set things right again.
None of the other games on this list near the perfection that is Bastion's iOS port. Supergiant Games went the extra mile by developing an intuitive touch based combat system that plays to its strengths but doesn't take away from the game's playability in any way. What's more, those who prefer traditional controls can switch to virtual buttons and play the game much the same way they would on an Xbox 360 controller at any time. Throw in some retina display, and the game looks better than it ever has.
Bastion's due to receive a spiritual successor, titled Transistor, in 2014, and it looks to be just as beautiful as Bastion. Here's hoping Supergiant Games takes the time to port Transistor over to iOS devices in the future.