Common devices that feature USB OTG -
Google/asus nexus 7
Samsung Galaxy tab 10.1/8.9 (Requires different OTG cable to other devices)
Samsung Galaxy S3/S2
Motorola Droid X
Sony Xperia (some models - Google your device model for more information)
LG Optimus (some models - Google your device model for more information
Many more devices feature this capability, if yours isn't listed Google your model number followed by "OTG"
USB OTG cable - This cord connects to your device and allows you to connect other peripherals (such as the controller). For this exercise you will require a male micro-usb to female USB cable. For the Galaxy Tab devices you may require a different male 30pin to female usb cable.