I looked at two world conquest-style games that follow from the original Risk board game: Strategy and Conquist. Admittedly, I'm not a big Risk fan. I much prefer games that involve more building and planning and less random dice rolling. With that confession on the table, I did find that both games were well made and offered many nice features.
For US$3.99, Conquist for the iPad offers an app that, of the two, is closer to real Risk. The map is the standard Risk world (see the screen shot above) and Risk-style grace notes like those cards you collect and trade in are included in game play. Conquist provides multi-player interaction using a single interaction board, so you don't have to "pass and play" your iPad around. If you don't have friends around, it's easy enough to set up two to five bots to play against.