There is an interesting SEO question that Google's Matt Cutts did a video answer for. The question was:
Many of my items belong to multiple categories on my eCommerce site. Can I place multiple breadcrumbs on a page? Do they confuse Googlebot? Do you properly understand the logical site structure of my site?
Here is the video answer:
Now, this is not uncommon. Often e-commerce sites have one product in multiple categories, and because of that, the breadcrumb (and URLs) may change. You should never have a duplicate URL for a product, unless you use the rel=canonical, but even then, try not to duplicate the URL. But the breadcrumb is for the user and to help them understand their click path and that may change based on the click path.
Most sites I see that are well optimized only show one breadcrumb trail despite the click path, which isn't always that great for usability. But Google's Matt Cutts said you can have multiple breadcrumbs on a single page, which is interesting and while Matt said it might help Google, it can confuse the user, I would think.
Matt also said they take the first one but might use the second and third one.
Here is an example from @sheknowsSEO with a site that has different breadcrumbs for the same product with a different click path. It would be this page vs this page - same product, slightly different URLs and different breadcrumbs:
Forum discussion at Google+.