Just the other day I mentioned Battle for Wesnoth in this very space, and then right after that, the game releases its 5th major update. If you like turn-based strategy games, this one is a must-have.
It was originally an open source title, and fans have added so much to the game that there are now tons of various units, six factions to play as, and campaign after fan-made campaign to play through -- over 300 hours of playtime in total. The latest update adds yet another campaign, a bonus tower defense game, OpenFeint integration and a whole slew of other features.
The iPhone version isn't bad, but I'd say the iPad version is better, as the bigger screen makes controlling the game a little easier. The game is US$5 on both platforms, and there's no free version, but the original title is still open source (which is why there are so many fan-made features), and available for a free download on the Mac. So go try out the game there, and if it's something you're interested in, consider supporting the iPhone developers.
Personally, I love Battle for Wesnoth -- while the graphics aren't exactly cutting edge, the strategy is fine-tuned by a whole legion of coders, and the fantasy setting and storytelling are great for a game of this kind. If you haven't given it a look yet, now's your chance.