There's been considerable discussion about the "broken breadcrumb" problem in Drupal. This occurs when you are displaying a node that isn't in your site's menu (usually of the type "story") and linking it from a taxonomy-based listing page.
For example, the path "taxonomy/term/4" will produce a list of nodes with the category term "4" and, if that taxonomy list is in the menu, the correct Breadcrumb. In short, it works.
BUT when you click on the title or "read more" for any of these nodes and the site then displays this node alone, Drupal's Breadcrumb "breaks".
In fact, it's not really "broken" and there's very good logic behind this behavior. Drupal draws the Breadcrumb from its menus and when a node isn't specifically placed in the menu, Drupal treats it as an orphaned node and displays it as a sub of Home. This is actually at the crux of Drupal's flexibility so that nodes can be categorized in many ways and displayed in different lists and screens site-wide.
Logical, but it doesn't help you very much. :-)
This is a solution to that problem that my colleague from May First/People Link Jamie McClelland and I worked up for some sites we're working on. It avoids hacking core or any modules -- which can be very problematic -- and is based on customizing the node template using a combination of Drupal's functions and some php code.
This solution has been tested with Drupal 4.7 (although it should work with 4.6) and uses examples from the box-grey theme although it will work with any theme I've seen.