Had a nice example of this just before Christmas. I was researching descendants of one of my great grandmother's sisters, and the names came down to a living person with a distinctive name. Normally doing a search for most names on Facebook is futile because there are dozens or hundreds of results with the same name. But in this case, the name came right to the top of the search list.
I sent him a 'friend request' and a private message explaining that we were probably third cousins, and he responded within a day or two. He passed the message on to his retired father, who then emailed me with a bunch of great new information and some really valuable old photos of the parents of this great grandmother, first photos of them that I had ever seen.