Lost Cities is one of Reiner Knizia's award-winning board games that recently made its way over to iOS, and I think it's great. The game is simple and easy to play, but it shows off quite a bit of complexity among just a few elements. The biggest complaints I have are that the tutorial can be confusing and there's no iPad version yet, unfortunately. But Lost Cities is an excellent strategy title good for quite a few matches of play.
The core game here is a card game. You deal cards of various colors and numbers out of a stack, and then place those cards in certain colored lanes or in a discard pile. Playing cards in lanes gets you points. Each lane starts at negative 20 points, so the player needs to try and put as many cards in a certain lane to make their score positive and higher than the other player. The trick, however, is that you can only put cards in lanes in ascending order. Placing down a card worth the max of 10 points will earn you those 10 points, but it will also block off adding any other cards to that lane.
Presentation is excellent: the graphics are clear, there's an excellent soundtrack and a variety of AI players to face off against. The Coding Monkeys, who also made the excellent version of Carcassone for iOS, have added "goals" to earn as you play, which offer extra incentive for replay value. Lost Cities is available for $3.99. It's a little steep as these games go, but if you like well-designed card and board games, it's worth skipping that cup of coffee to buy.