The official Xbox 360 controller by Microsoft.
Ranked in these QuestionsQuestion Ranking
Pro Plug and play
Works out of the box as Android recognizes USB peripherals. You will need a USB OTG cable (can be found online for $2-3 usually) to power the controller, but once you have that it's just plug and play.
Pro Good value for money
The wired controller is often sold under $30, but feels solid.
Pro Great design
XBox controllers have inimitable quality and design. XBox controllers feel substantial in the hand, and are comfortable to hold onto for hours on end.
Pro Good availability
You can find it almost everywhere. Easy to find and purchase.
Con Requires a USB dongle for wireless
In order to use the controller wirelessly, you will need the Xbox 360 wireless dongle adapter, although it doesn't work while charging. A USB OTG cable will still be needed.