Chris Riley has posted an interesting site to the backstage mailing list: BBC Touch. What the site does is compare the news stories on the front page (which are described as the stories the beeb 'wants' us to read) and compares these with the most popular (most read) stories based on the most read stories RSS feed (this is described as the stories 'we' want to read). On top of this, some key term extraction is done via the Yahoo term extraction API.
The site is definitely fun, however, one needs to have a bit more perspective as to the function of the BBC and its relationship to other news media services. Research by Ethan Zuckerman demonstrated that the global coverage of the BBC news (that is to say, the distribution of countries in articles published by the BBC) is quite different from that for other (US based) media. Note that currently, Ethan is not supporting his Global Attention Profile research page, so you may have to dig a little to get the details. Secondly, one has to be careful in interpreting popularity. The BBC has a clear obligation to provide informative and broad coverage to the nation (and the world). Guiding news via popularity is in part an admission of news-as-entertainment which is a very slippery slope. Remember the BBC is not a commercial enterprise.
One could almost look at this site as indicating how in touch readers are :-)