Do Xbox One controllers support Xbox 360 games on PC?

On a PC there is no difference in games between Xbox 360 and Xbox One controllers- both work the same.

The only thing you should keep in mind is that an Xbox controller will have "weird" layout or even completely refuse to work in very old games that use DirectInput, rather than XInput, but that won't differ between Xbox360 and Xbox One controllers either.

For 99% of cases, no, it won't matter.

However, I've tried to go back and play some legacy games with the Xbox One controller (which I knew worked with the Xbox 360 controller). Two of them had some very strange problems with the dead zone of the joystick. Even stranger, on one of the games, the problem was solved using the USB driver version rather than the wireless driver.

Again, this would only happen 1% of the time on the lower-budget indie games. So, if your that concerned, pick a few of your favorites and Google "[game] Xbox one controller problem".

Games that support the Xbox 360 controller use xInput (a library created by Microsoft) to interpret the inputs from the controller into in-game actions.

The Xbox One Controller uses the exact same xInput settings as the 360 controller, so to a game the two controllers are no different.