Generally games will say if they support controllers, for example Guacamelee: http://www.gog.com/game/guacamelee_gold_edition
Says this in the details: Controller support: Supports the Xbox 360 Controller and other XInput-compatible controllers.
When in doubt, check the game's forum page, and ask if the question isn't already presented.
I believe you can also use a wrapper that maps keyboard keys to your controller keys, you should be able to find something like that through Google. examples, JoyToKey, Xpadder...