As a genealogist blessed with a considerable trove of ancestral data, I know where to find those convoluted lines in my family tree that show how I connect with various European nobility and even, if royal pedigrees are to be believed, to such fine fellows as Erik Bloodaxe, Lady Godiva and Old King Cole. But then, if you have European ancestry, so do you.
Martin Rundkvist lays it on the line at Aardvarchaeology:
"Do the math as you count generations into the past. Two parents, four grandparents, eight great grandparents, sixteen great-great-grandparents, and so on through the centuries. Soon you reach a point where the number of ancestors in a given generation is larger than the population of the Earth at the time. (This is possible because as you move back, a single individual may occupy a large number of slots on your family tree, which is known as pedigree collapse. That is such a badass term.)
The population of Europe in AD 1000 is estimated at about 36 million. Not all of them had kids. With a mean generation length (defined as the duration from a person's birth to the birth of their first child) of 25 years, we get 40 generations per millennium. 240=1,099,511,627,776. There are almost 1100 billion slots on your tree in AD 1000. So all living Europeans and European-descended people elsewhere are descendants of Saint Olaf."
This also means that if someone calls you a "royal bastard", strictly speaking that is probably true even if you don't know for sure where in your lineage you link back to one of Henry Plantagenet's innumerable litter. The fact that so many of us with a drop of Caucasoid DNA in our veins do know where to find the links in our ancient ancestral chains has a lot to do with the higher survival rate of the nobility (there is the little matter of the Black Death creating something on an ancestral bottleneck) and because there is better documentation of the ruling classes and their progeny, along with subsequent interest (snob value) by more recent generations. Each generation and global movement of our species merely increases the likelihood that we will have more ancestors in common. And if you go far enough back, say 70,000 odd years ago, a massive supervolcanic event at Lake Toba in Sumatra is theorized to have reduced the entire human population to 1,000 breeding pairs.
DNA sequencing , of course, means that genealogists don't need those 800 year old parish records to have survived Cromwell or the Blitz to prove that you are related to ancient people from some specific European local. There is, for instance, the case of Cheddar Man, Britain's oldest complete human skeleton, who lived around 7150 BCE. That is 300 generations ago, and yet after mitochondrial DNA was extracted from one of his molars and compared with samples from 20 living residents of Cheddar Village, it produced 2 perfect matches and one with but a single mutation.
Because they used mitochondrial DNA which is passed exclusively from mother to child, these closest living relatives may be descended not from Cheddar Man but his mother or sister. Geneticists conclude we all go back to a Mitochondrial Eve about 140,000 years ago through our mothers.
"To find the Mitochondrial Eve of all living humans, one can start by tracing a line from every individual to his/her mother, then continue those lines from each of those mothers to their mothers and so on, effectively tracing a family tree backward in time based purely on mitochondrial lineages. Going back through time these mitochondrial lineages will converge when two or more women have the same mother. The further back in time one goes, the fewer mitochondrial ancestors of living humans there will be. Eventually only one is left, and this one is the most recent common matrilineal ancestor of all humans alive today, i.e. Mitochondrial Eve.
It is possible to draw the same matrilineal tree forward in time by starting with all human female contemporaries of Mitochondrial Eve. Some of these women may have died childless. Others left only male children. For the rest who became mothers with at least one daughter, one can trace a line forward in time connecting them to their daughter(s). As the forward lineages progress in time, more and more lineage lines become extinct, as the last female in a line dies childless or leaves no female children. Eventually, only one single lineage remains, which includes all mothers, and in the next generation, all people, and hence all people alive today."
This common female ancestor of ours is the source of the only purely matrilineal line that survives in our human tree.
So much for the blood of kings. It is quite common after all.