With the advent of iOS 7, support for controller add-ons was born -- it just took a while for them to actually come out. They're officially known as MFis (made for iPhone), and they basically allow you to snap your device into them to allow for tactile buttons. Your options are limited for now, as there are only two official controllers on the market -- the MOGA Ace Power, and the Logitech PowerShell, which both retail for $99.99.
I'm currently testing out the PowerShell, but in the meantime below is a non-exhaustive list of all the games that'll work with your shiny new peripheral. If you find any more that indeed support iOS 7 controllers, feel free to list them here. This list is non-exhaustive.