Hello,

I often use PHP includes on my sites. However, a site I am working on is on a server that does not have PHP capabilities. Is there a way to do what php includes does but using javascript?

Not really...
Javascript is a process executed in the browser, PHP is a process executes on a server.

PHP can access files on the server, receive upload, connect to database, create or modify images.
Javascript cannot do any (or almost) of those.

I'd suggest you to get your site hosted on a server which include PHP.
Shouldn't be that hard...

I'm not sure exactly what you are asking here. If you are wanting to include other JavaScript files dynamically with JavaScript, then yes, it is possible.

var scriptSrc = 'example.js';
document.write('<script type="text/javascript" src="' + scriptSrc + '"></script>');