You have to modify the Xbox 1's controller, but the Xbox 360's controller uses USB. The wired just plugs right in while the wireless controller requires the wireless receiver (as a bonus, it can detect up to 4 controllers like the Xbox 360). Microsoft should have updated drivers every so often for it and games that support a gamepad will support the Xbox 360 controller. I've been using it to play Resident Evil 4 on PC.
Any game on Games for Windows should support the Xbox 360 gamepad as long as it uses it. Halo 2 Vista is a prime example.