Just the other day I was talking about more in-depth strategy games for iOS, and here's one: Great Little War Game is a pretty deep tactical warfare game built specifically for Apple's platform. It's based on what's essentially a hexagonal system and is very similar to Advance Wars for the DS, with cartoony little troops fighting little tactical battles. There are a few different types of units and goals to play with, and while the game's technically a little off, the gameplay is extremely solid, with clean and clear controls and lots of strategies to use and learn.
The game's model is interesting as well -- there is a core campaign (and a lite version to check it out for free if you'd like), but there are also add-on packs with extra missions to play or voices to use for the characters if you'd rather have those. There's no Game Center integration or multiplayer, unfortunately, but the core single-player strategy gameplay is what most fans of this type of game are looking for anyway. Great Little War Game definitely lives up to its name. It's available on the App Store for an introductory price of US$0.99 for the standard iPhone version or $2.99 for the HD universal version for iPad and iPhone.