While you can go down the long, perilous road of obfuscators, you generally don't see them used on real, production applications for the simple reason that they don't really do much. You'll notice that Google apps, which is really a whole heap of proprietary and very valuable JavaScript when you get down to it, is only really minimized and not obfuscated, though the way minimizers work now, they are as good as obfuscated. You really need to know what you're doing to extract the meaning from them, but the determined ones will succeed.
The other problem is that obfuscated code must work, and if it works, people can just rip it wholesale, not understanding much of it, and use it as they see fit in that form. Sure, they can't modify it directly, but it isn't hard to layer on some patches that re-implement parts they don't like without having to get in too deep. That is simply the nature of JavaScript.
The reason Google and the like aren't suffering from a rash of cut-and-paste competitors is because the JavaScript is only part of the package. In order to have any degree of control over how and where these things are used, a large component needs to be server-based. The good news is you can leverage things like Node.js to make it fairly easy to split client and server code without having to re-implement parts in a completely different language.
What you might want to investigate is not so much obfuscating, but splitting up your application into parts that can be loaded on-demand from some kind of service, and as these parts can be highly inter-dependent and mostly non-functional without this core server, you can have a larger degree of control over when and where this library is used.
You can see elements of this in how Google is moving to a meta-library which simply serves as a loader for their other libraries. This is a step towards unifying the load calls for Google Apps, Google AdSense, Google Maps, Google Adwords and so forth.
If you wanted to be a little clever, you can be like Google Maps and add a poison pill your JavaScript libraries as they are served dynamically so that they only operate in a particular subdomain. This requires generating them on an as-needed basis, and while it can always be removed with sufficient expertise, it prevents wholesale copy-paste usage of your JavaScript files. To insert a clever call that validates document.href is not hard, and to find all these instances in an aggressively minimized file would be especially infuriating and probably not worth the effort.
