Most takes on real-time strategy for the App Store have to corrupt the form in some way, yet some still turn out well (see Total War Battles for a a great RTS game that takes a different turn). But Amoebattle impressively does RTS as you expect it. You choose units, send them around exploring, and tap to attack or move through the fog of war in real-time.
There are nine different unit types to be discovered during the campaign, and each has its own attributes and abilities. The graphics are cute and colorful, but the tactics are hard to master -- especially near the end, when the game has no shortage of challenges to overcome.
Amoebattle is an excellent RTS title for Apple's touchscreen devices, something that a lot of RTS fans have dreamed about ever since the iPad was first announced. It's not perfect, but it doesn't skimp from RTS traditions, even on a mobile device, and it holds up to them well. The game is US$4.99, in a universal version, on the App Store now.