Puerto Rico originated as a German board game) and has made the leap to iOS. It'ss a multiplayer strategy game that allows players to assume a different role in each round so everyone gets a chance to try something new.
In this game, you're a colonist trying to grow crops on a plantation in Puerto Rico, which you will then sell or ship to another destination. You also build a city that provide goods and other functions that aid you in creating a productive farm and eventually govern the island. In solo mode, you're playing against two computer-generated characters. Throughout it all, you're trying to earn victory points in your quest to gain dominance over the island.
Puerto Rico makes the transition to the iPad pretty well, and Ravensburger does a great job with the graphics, though the game controls are a bit fuzzy and hard to deduce. I highly recommend going through the extensive tutorial before playing the game, especially if you never played the original board game. Even after going through the tutorial, I found myself relying on in-game hints until I got used to the controls and gameplay. It's a challenging, fun game and the iPad version is available for $7.99.