I cannot say enough about Monument Valley. It is piece of art in itself. You play as a small princess, wandering through an Escher-esque landscape, solving puzzles. The storyline is a bit weak, but the artwork, colours and music will win you over. It only took me one day to finish all 10 levels, but definitely one to play with the headphones on.
Currently available on iOS ($4) and soon to be released on Android.
A screenshot from level 4