Yes the xbox 360 controller works with windows and games that support it. If you are running vista or windows 7 it will install the 360 controller drivers for you when you plug the controller in.
See this pagefor more details and software download for other versions of windows.
As far as the controller working with SG, I have no clue. Games for windows that work with the controller have built in support for it, SG does not have built in support for the 360 controller. You might be able to map the controller buttons but I have never tried it, I don't game on PC anymore..