That depends on the kind and quality of gaming you are planning on doing. If you are looking for raw power (which translates to very smooth gameplay on large screens), then its impossible to go wrong with the Samsung Galaxy SIII or the HTC One X. The only phone to date that I know of to have a controller built in is the Sony Xperia Play. The controller is (quite obviously) based around the Sony Playstation controller. Unfortunately, the hardware in the phone is a year or so old (ancient in the smartphone world). Because of that, I would recommend the first two phones, and buying a bluetooth controller.