Here's a browsable example API: http://rest.ep.io/
Because your browser provides Accept: text/html by default you get back a nice html page describing the result for the API root. If you send Accept: text/json (click "json" at the bottom) you get back a json response.
You can follow the links in the html response to get to other parts of the API. You can also click "OPTIONS" to send an OPTION request to get a description of what you can send to that endpoint.