What are the advantages of creating web pages with XML instead of HTML?

From time to time, I see web pages whose content is solely written in XML (not HTML or XHTML). These pages usually have some style sheets (either XSLT or CSS) attached to them which makes them look like any other ordinary web page.

My question is, what are the advantages of such an approach (if any), and why would anyone choose to work this way?

EDIT: If this is a good thing, why is it not widespread?

EDIT 2: Thanks everyone for the great responses. They really enlightened me. I also found this question whose content is also related.