I am puzzled. A great many American family historians claim that they are descended from Charlemagne, William the Conqueror, Sir Isaac Newton, Shakespeare, Alexander the Great and other such famous names - I have seen the Charlemagne claim many times - here is one such website devoted entirely to delusion http://www.geocities.com/EnchantedForest/Pond/7984/krslgst.html .
I am particularly amused by those who are "descended from" Richard the Lionheart and Elizabeth I, neither of whom ever had children.
Either "professional" genealogists in the States operate like fortune tellers - you hear what you wish to hear - or the descendants of almost everybody famous simply picked up sticks and went across the Atlantic. Why do the Americans, who grabbed independence well over 200 years ago, strive so hard to prove they are really British?
Why do none of these people with fabulous pedigrees claim kinship to Attila the Hun or Vlad the Impaler or Dr. Crippen? That might be more credible! 
I can only speak for
this American. It's been my experience that most American genealogists aren't necessarily trying to prove royal, or even English descent, we just want to know
who and
where we came from. Unless one is a pure Native American, (formerly referred to as "Indians"), then every American is either an immigrant themselves, or descended from someone who emigrated here within the past 400 years. And it's the immigration records that make going beyond recent history so tricky. When we are able to succeed in struggling through the immigration records and tracing our ancestors to some place across the pond, it's a real accomplishment.
One possible theory as to why I think many people claim descent from famous folks is that the hard work has already been done for us -- the genealogies of the famous are well documented and readily available, and it therefore only takes making a connection to a recent ancestor to "hook into" the line of a more distant and perhaps famous (or infamous) one.
Recently, to our utter surprise, a cousin traced our Loper great-grandparents on my mother's side back to King Henry II and Eleanor of Aquitaine. Eleanor and Henry are our 22nd great-grandparents. Eleanor is
supposedly descended from Charlemagne (still a bit sketchy on that one -- still some work to do there), so we list him as a
possible ancestor of note, without yet having that lineage worked out completely. It just makes for fun conversation when the family gets together.
But that's all it really is -- a fun conversational topic within the family. What would mean much more to us is if we could trace our lineage beyond my father's grandfather. That branch of the family tree stops with him and has proven incredibly difficult to trace. If I were able to find out more about him and determine the names of his parents, grandparents, etc., it would mean so much more to me than this English royalty. I'd gladly throw back all that English heritage to gain more information about my Danish ancestors.
And regarding relationships to more shady, infamous folks, we haven't yet found evidence of a relationship to Attila the Hun, but my sister-in-law is descended from Dr. Mudd, the physician who set John Wilkes Boothe's broken leg after he assassinated Abraham Lincoln. Mudd's name truly
is mud in America!
-Mary
