Originally Posted by GoofyJmaster.
Starbase Orion...bar none!
If yer looking for a very deep, sophisticated async experience, with long matches, in-depth turns and micromanagement aplenty, GoofyJmaster has the truth of it: there is nothing even remotely close to Starbase Orion for iOS. The game is basically a real desktop-class 4X game, not far from Masters of Orion and Civilization. Colonize and conquer the galaxy through military might, economic expansion or espionage (with diplomacy on the way), design and produce your own ships, customize your own race before the match, research techs, build buildings, and use ship-specific orders before battles to change the outcome (which makes for a surprisingly deep passive battle system).
It also enjoys some of the best developer attention and support on the platform (or probably on any platform). Rocco (the single dev) sends out new betas several times a week, and app store updates probably once a month. These updates do far more than just polish the game: so far, he has added new ship systems and weapons, new techs to be researched, leaders with specific abilities for colonies and ships, new async functions, options for customized games, user-configurable build queues that are saved for future matches, and plenty of new in-game functions (from auto-upgrading of old ship equipment, ship naming and fleet summaries to tons of convenience features and UI improvements).
With diplomacy and more advanced win conditions on the way, my guess is that Starbase Orion will grow for a long time. But, regardless, what is already there is a far more advanced async experience than anything else.