Depends a bit on the game, but recently, I use almost exclusively a Dualshock 4, which is supported natively in pretty much every recent Mac game (at least the ones from Feral and Aspyr). Steam itself also supports it for Big Picture mode.
Logitech F310; has a switch between regular USB gamepad mode and Xbox 360 mode, so it works with all games that support controllers. Mostly I leave it in Xbox 360 mode, since otherwise the left/right triggers just act as buttons. However not all games work with it in that mode.
Steam and GOG don't have anything to do with controller support, other than Steam's big picture mode as mentioned above, which still has nothing to do with individual games.
Steam and GOG don't have anything to do with controller support, other than Steam's big picture mode as mentioned above, which still has nothing to do with individual games.
You could actually use Steam to configure controllers for any game. The option is a bit hidden in the Big Picture preferences, is somewhat rudimentary (essentially, you bind controller buttons to keyboard keys) and it often interferes with the controller support built-in many games, but it's there.