Microsoft just released the PC drivers for the Xbox One controllers. They will be packaged in with an upcoming Windows update however, you can download them now on Major Nelson.
Any game and application that supported the Xbox 360 controller, should support the Xbox One controller as well.
We know our fans have wanted PC compatibility, and we know they wanted to be able to use the Xbox One controller with the same games and applications they have been playing with using the Xbox 360 controller. [...] The new PC drivers will enable the Xbox One controller to be used with any game that featured gamepad support for the Xbox 360 controller. Simply download the drivers, connect your Xbox One controller to your computer through a micro USB cable and you’ll be gaming in no time.
If you game on PC using any kind of controller, I highly recommend upgrading to the Xbox One controller. It's incredibly comfortable and offers great haptics.