My relatives would sometimes talk about how we were related to some deposed king or some princess who ran away to avoid being married. I thought it's likely there's enough princesses and undocumented deposed kings out there that everyone should have a great-great-grandaunt who was a legitimate princess in their lineage. This article supports that theory.
Even more interesting IMO is that the same argument holds not just for royalty but also for religious figures whose descendants have special divinely-sanctioned status in various different religions. For example, it's quite likely that we're all descendants of the original high priest Aaron, whose descendants and no-one else are allowed by God to perform certain actions (caveat: the ancient texts are ambiguous about whether "descendant" means "descendant along both maternal and paternal lines" or whether it's more restrictive, and in certain circles this could be a sensitive question). Similar thing for religious prophecies about peoples' descendants (e.g. that the Messiah is a descendant of Judah---it's probable that we are all descendants of Judah by now).