This is a case of tradeoffs, with no single best solution.
For example, if your http://example.com/ provides content through a standard web interface as well as through the API, then you need something like http://api.example.com/api//
just to separate browser-based application access from API interaction. Does this make sense?
Example: api.rottentomatoes.com
However, even if your domain is dedicated for API calls, it’s meaningful to use the above pattern anyway, and reserve http://example.com/ for other ways of interacting with your application. For example, you might want http://example.com/mobile/, etc.
