1. Monument Valley
This devilishly clever game, which costs $3.99 (USD), won a prestigious Apple Design Award this year. The player guides a silent princess through an Escheresque world with strange physics, hidden passageways, and more. Monument Valley may sound strange, but it's one of the most beautiful and challenging games ever to hit the App Store.
It uses the iPad's touchscreen perfectly, with an elegant soundtrack that deserves headphones. The game isn't particularly long, lasting a little more than an hour, but it is one of the best games ever released on the iPad.