Our friends over at AndroidNZ went through and did a nice review of the Samsung Galaxy S III phone. When doing their reviews they also like to test out controllers, mostly because the crew over there happen to play a lot of Android games like we do. Good news is a few controllers work right out of the box.
First off the Nintendo WiiMote works nicely over Bluetooth on the stock ROM that the SGSIII comes with. This means there really shouldn't be problem with any other Bluetooth controllers you may use when playing those fancy games on your Android device. Also, you will be able to use two wireless bluetooth controllers simultaneously for when you are playing games with a friend, as long as the game supports it. However, running two controllers did have a few hiccups.
Playstation 3 controllers are also confirmed to work over USB OTG. However, some wired controllers do not work with the SGSIII including the Xbox 360 controller and the Logitech F310. So a little good and a little bad news for those of you considering getting an SGSIII and happen to do a lot of gaming with controllers. Of course most of this is solve with rooting anyways.