A HighRankings Forum thread has discussion on how useful the breadcrumb trail / navigation is for your SEO strategy.
Most people agree that having them from a usability standpoint, makes total sense. So, for users, it makes sense. But does it benefit your on-page SEO? I would think most SEOs would say, it does.
In fact, one of the ask the SEOs panels (forgot which one) at SMX East, all the panelists agreed that breadcrumbs are so easy to add and can add a tremendous amount to your on-page efforts, you should 100% spend the time to get them implemented.
If you bring up the old topic of is the first anchor text link the only one to count, then it is a matter of how you handle the CSS placement of those links in your HTML source. But overall, I think every SEO would say, that in most cases, having that breadcrumb navigation wouldn't hurt and can benefit on some level, if done right.
Forum discussion at HighRankings Forum.