We're using ReadMe.io for our public API (which has been in closed Beta forever), you can see the docs here: https://docs.stackshare.io. They've got all the stuff you'd expect: custom domain support, lots of integrations, etc.
The design looks great and having the actual JSON responses on the right side panel is really nice. My favorite feature is the API Explorer which allows you to test out real API calls once you've entered a key.
We haven't really promoted the API since we're not opening up access just yet, but once we do I know ReadMe's got us covered!