This Bluetooth Game Controller from Allputer works with iPhones and even iPads. (Allputer says it has a known problem with Android devices running Android 4.0, but it should be compatible with devices running some other versions of Android.) The controller has a telescoping holder at the top to hold your phone in place, or you can use it with a tablet. It has a rechargeable internal battery for long game play, and it connects to phones or tablets via Bluetooth 3.0. Allputer says it should be compatible with a variety of games; check the item’s webpage for a list of games and how to set up the controller for various types of games.
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