My experience has been this.
Last year, Google scrambled to implement mark-up fully. Much of what Google suggested on it's site did not work or was not implemented and that frustrated early adopters. Google did a fantastic job of implementing mark-up and the work was done extremely fast. Today, it seems that mark-up works as advertised.
Prior to that, I found that bread-crumb style of links not using mark up could be picked up but not always fully understood- it would have to be simple. I had an unordered list of links that Google displayed but that may not have been intentional on Google's part.
Today I use the example I gave here: Breadcrumb using Schema.org rich snippets and I cannot tell you if simple links still work. In fact, I should update how I use bread-crumbs based upon Google's examples.
I suggest using mark-up. Google does not guarantee that they will display bread-crumbs. This is unfortunate.
The theory behind using mark up to display bread-crumbs for Google was that the additional links increases the user experience and can satisfy the search users ability to find what they are looking for. I am not sure that is always the case. It depends upon the bread-crumbs. I found that even though almost 600,000 pages had bread-crumbs, Google would only display them for a number of the pages. The results were disappointing. This, for me, was not a problem since I did not create the bread-crumbs for Google but users.