I would have to agree with Jared that breadcrumbs are most useful to tell users "where they are" - location breadcrumbs - when they "teleport" to a deep page within a site.
For example, this page on Star Trek teleporting has a breadcrumb that makes it pretty easy to see where I am within the sciforums site. For this BBC article on teleporting without a breadcrumb, it is harder to tell at first glance if this article is actually "science" or "tv".
The jury is still out on attribute breadrumbs. In database-driven sites, there often is not 1 "true" location for a piece of content. What I call "attribute breadcrumbs" - a list of locations for a given object - might help out here. For example, the attribute breadcrumbs for this book on teleportation tell me at a glance that this book is more about spirituality than science. In a real bookstore, there is 1 place on the shelf - attribute breadcrumbs show all of the locations the book may have been placed. We need some research here to see if/when these breadcrumbs help.
There does not appear to be as much value for path breadcrumbs on sites. The browser does an acceptable, but not perfect, job of keeping track of a user's path.
Anyway, designing a page that stands alone and does not require the user to start at your site home page has always been wise. Breadrcumbs are one tool at your disposal for this.