When I started doing genealogy research, I got a postcard from one of my relatives suggesting that there might be a connection to Mary, Queen of Scots. For the entire time that I had known of this family legend, I thought it was a bit too unlikely to possibly be true. After all, I had only this one postcard to go on for this story, and I haven't seen anything in the rest of my research that might suggest a connection. So I haven't really tried to prove this connection with very much vigor at all. The closest that I've seen was in the 1925 history of Alexander Meharry's descendants, where it mentions that the Meharry line emigrated from Scotland to America as a way to flee religious persecution during her reign. It may not be as glamorous a connection as a blood relationship, but this is one explanation that I can believe.
However, in looking around on a different topic this week, I found many resources that show a probable blood connection to another very well known British leader. He wasn't an ancestor, but turns out to be a cousin. Sir Winston Churchill (b. 30 November 1874; d. 24 January 1965), Prime Minister of the United Kingdom in the 1940s and 1950s, was descended from Mehitabel Beach (b. 1749; d. 1807), who connects into my Beach line through her great, great grandfather, John Beach (b. 1621; d. 6 November 1677). John was the first of the Beach line to live in North America, and making the leap back to the British Isles has proven very difficult for a number of researchers. I'm still digesting the assertions and trying to fit various people into my lines. So now I have another avenue to research in proving my distant Beach relations.