When a web page with inbound links is deleted, the PR (Page Rank) which it previously received from those pages goes instead to the 404 page which the user receives.
This should provide further motivation to make your 404 page useful and informative. A 404 page should optimally tell the user about your web site and help the user to find the information he or she is looking for.
A good 404 page should include a site search function and a site map.
The proof that the PR (Page Rank) transfers to the 404 page can be seen by finding 404 pages with high PR's. Presumably, no on is intentionally linking to boring generic 404 pages!
One 404 page which provides strong evidence in support of this theory is http://www.geocities.com/CapitolHill/Lobby/3198/, which is currently a PR5. Of course, it's PR may go up now that we are mentioning it!
Thanks to Martin Hagstrøm for solving this riddle!