controllerssteam
For Big Picture Mode, they always advertise on the game's Steam page that it supports full-controller or partial-controller. Next to that they show a picture of the Logitech F710. I know that they do support the Xbox 360 controller for Windows.
Are these the only controllers that Steam supports or are there more?
Do'h! Looks like I just needed to restart Steam (even though I had already gotten the update...)
Then the "Big Picture Mode" button is hard to miss - it's in the upper-right of the Steam UI.
The Big Picture Release Sale page on the steam website has an answer. Here's a screenshot of the right hand side from that URL:
And here's the text for completeness:
Full Controller Support
Games with Full Controller Support will work without a mouse and keyboard on hand, from installation to play and beyond.
Partial Controller Support
Games with Partial Controller Support may require a keyboard and mouse from time to time, during installation or for limited interactions.
So, basically, it would appear that a game with full support never needs input from anything that isn't a controller, whereas games with partial support can mostly be played with a controller but you'll probably need a keyboard and/or mouse to do something at some point (which might just be to click 'OK' on a window to install DirectX or enable controller in options on the first run or maybe click 'Play' in a launcher every run, etc).
Best Answer
Officially, Steam Support states support for the following.
In addition, you can infer support for a variety of third party gamepads that offer similar button layouts and drivers - for instance, any third party Xbox compatible gamepads should work just fine.
With the use of third party drivers like MotioninJoy, a variety of other options are usable as well, though unsupported.