This page demonstrates some of the bits in a page that are affected by !doctypes. It does not attempt to provide examples of everything affected, and in some browsers you may not see any differences. View the page in (at least) Internet Explorer and FireFox.
The iFrames below show the page content - first with a valid, complete doctype, and the second with no doctype. These links to the pages open in new windows, so they can be compared as pages outside the iFrames.