How can I use an Xbox 360 controller to play Steam games?
In the Store page of every Steam Game you can check if one of these symbols is available.
Usually in all recent games (2-3 years), if a controller is enabled, there are high possibility that Microsoft Xbox 360 works and is well supported.
But to be sure I always suggest to take a look to that game specific forum. Most of times there are users that already asked for Xbox 360 compatibility.