There is a beta Javascript client library for the Gmail API [0]. If you are looking to interface with an API that doesn't provide a JS client, your best bet might be to just build yourself a simple client using jQuery to handle the HTTP communication (see, for example, jQuery.ajax [1] for making HTTP calls).
ETA: To elaborate a bit, "interfacing with an external API" is usually just a fancy way of saying, "making HTTP requests." In Javascript, this means using the XmlHttpRequest browser API, which people call AJAX because it sounds hip. You can use it directly, but jQuery gives some extremely convenient helper methods for easily composing requests. One thing to keep in mind is that if the API uses JSON, you will have to consider that the browser does not permit you to return JSON from a cross-domain request (which an external API call almost certainly is). There is a way to enable this using something called JSONP [2].
ETA: To elaborate a bit, "interfacing with an external API" is usually just a fancy way of saying, "making HTTP requests." In Javascript, this means using the XmlHttpRequest browser API, which people call AJAX because it sounds hip. You can use it directly, but jQuery gives some extremely convenient helper methods for easily composing requests. One thing to keep in mind is that if the API uses JSON, you will have to consider that the browser does not permit you to return JSON from a cross-domain request (which an external API call almost certainly is). There is a way to enable this using something called JSONP [2].
[0]: https://developers.google.com/api-client-library/javascript/...
[1]: https://api.jquery.com/jQuery.ajax/
[2]: http://json-p.org/