This article on the distant relations of the presidential candidates makes me laugh. Especially when it includes such things as tenth cousins, twice removed. My oldest brother is the one in our family who has put the most work into tracing genealogies, but I'm fascinated with them as well. Our approaches are quite different, though. What he's generally done is take a particular ancestor of ours and then trace that line forward to all the descendants alive today. I'm more interested in tracing the lines upward, finding how far back I can get on any given line (and then imagining what life must have been like for those people). Both approaches, of course, are essential for any complete genealogical survey, and for the information in this article, both were certainly used.
I don't know of any famous people I'd be related to, even distantly. Most of my ancestors came over on da boat from the Netherlands anywhere from 1890-ish through 1912. (My maternal grandfather recalled leaving port the day after they received the news that the Titanic had sunk.) My brother has traced descendants of most of these families pretty extensively, and I don't remember any famous types from there.
Because my paternal grandmother was adopted, though (by a paternal aunt and uncle who were Dutch immigrants, so we knew that side), there was one line that was a mystery until I discovered online genealogy sites back in 2000 or so. Then I was able to trace that line back to pre-Revolutionary colonies. (Pennsylvania, I think, though I'd have to double-check that to be sure--I wonder if they were Quakers? that hadn't occurred to me at the time, but they seem to have been from Shropshire, England. Anyone know enough about Quaker history to know if that makes it any more or less likely? And their descendants sided with the North in the Civil War strongly enough to name my great-great grandfather, born during the war, Joseph Union, despite living right on the line between north and south, which would fit with Quaker anti-slavery movements...) Anyway, that would seem to have more potential for getting me (distantly) related to people who have been famous in the US.