I know this is a bit of an older question, but browsers changed, and right now, it is possible to do what the poster requested. This means that most of the other answers are no longer valid. I'm posting a way to accomplish this so that it might help people using Google to find the correct answer.
In short, on modern browsers (browsers with HTML 5 support) you can. Please have a look at this article.
It basically boils down to the following line of code:
window.history.pushState("object or string", "Title", "/new-url");
Executing the above code will change the URL to example.com/new-url, and will help you accomplish what you wanted.
For a demo, you can take a look at the Webby Awards, where this method is used. Just scroll up or down and look at the address bare. The effect is pretty impressive.
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