As stated, it's pretty much always going to work, although I do suggest for games like shooters you try using the mouse. I definitely use a gamepad for some games but it just depends on which plays better, I prefer a mouse most of the time.
Also just FYI, if you like PS3 controllers you can use one of those as well with a program called MotionInJoy(.com). It's a free software that provides drivers for the PS3 controller. I use it with it set to emulate the 360 controller, since most games have default configs for the 360 controller. Saves time trying to manually make a profile, just gotta remember that X is A, O is B, etc.