It's now possible to use an Xbox One controller on your PC. Microsoft released PC drivers for the controller on Major Nelson's blog today.
Games that already natively support the Xbox 360 controller will seamlessly support the Xbox One controller, as well.
You cannot, however, use the existing wireless dongle to use the controller wherever you'd like. Instead, the Xbox One controller must be connected with a micro USB cable to your PC.
That last wrinkle means it's not much use to me, but I'm glad to see support's finally arrived.