As with almost all on-site factors, the answer is yes and no. Yes because they do have an impact, and no, because in the great scheme of things, that impact is quite limited. However, they can be great with helping your users navigate your site, especially if you have a deep site structure, so there’s no reason not to go for them.
However, it is important to note that, as with meta descriptions, having breadcrumbs on your site will not affect rankings. They just help Google to make a flashier rich snippet for you in their results pages, and that might just get you a better click through rate too.
They should reflect your web site’s structure, not the pathway that the user has taken through your site so far (so perhaps they should be called something else… oh well). Google has lots of information on how to implement them here: