From The Economist:
Despite all these difficulties, the world’s libraries have tried for over a decade to conserve some aspects of their national digital heritage. America’s Library of Congress started its digital-preservation programme in 2000 with $100m from the government. Its web archive currently stands at around 10,000 sites, many of them owned by the American government, and therefore exempt from copyright. Privately run sites are more difficult to include. For some archiving projects, only a fifth of webmasters reply to e-mails seeking permission for a copy.
Read the Complete Article
Btw, while there are many challenges to preserving the web, many exciting projects exist. It would have been nice if The Economist would have linked to some of them and/or a directory of projects.
Of course, you can learn about many of these projects and more about web preservation in general from the International Internet Preservation Consortium.