Stoneship was released earlier this year exclusively on the App Store, and it's got quite a pedigree. It was created by Cyan Worlds, the creators behind the classic game Myst, one of the most-loved PC games of all time. Unfortunately (or fortunately, depending on your gaming tastes), Stoneship is a completely different game. While there are some elements of exploration and puzzles to solve, Stoneship is much more of an arcade title than straight adventure.
In Stoneship, you are the captain of a British frigate, and it's your job to not only explore a series of Caribbean Islands but also set up and defend them against the invading pirate hordes. When you start a map, you get a set number of turns to split among exploration, creating and transferring defenses around, and fighting various findings on the map. After those turns end, you have to defend against a set of pirates; if you haven't moved your troops to the right places and cleaned up the map enough, you might lose all of the great towns you've built up.
It's an interesting game, but it's kind of lame that things are mostly out of your hands (you do press some buttons to actually run the battles, but mostly you'll make or break them early on). It's also a little frustrating to always have that turn limit knocking at the door, but the game is well-produced and good fun. It just recently got a clean-up update, and the next update is supposed to bring Game Center integration and a few more goodies. If you're willing to put a little thought into the way you play, check out Stoneship on the App Store right now for US$2.99.