Queen Elisabeth II from Genghis Khan:

http://www.pcug.org.au/~ronwells/Elizabeth.htm

Prince Charles from Persian Achemenides:

http://www.pcug.org.au/~ronwells/Charles.htm

note: it can be traced in some other line to the Greek Heraclides whose family legend says they're descended from Hercules ;)

Lady Diana from Attila the Hun:

http://www.pcug.org.au/~ronwells/Diana.htm

Here's the trick: the genes ancient Eastern dynasties back even to Assyria and Babylon survived in the Parthian kings. They mixed with the Seleukides, who also carried the Ptolemeian descent. Some of families related to those houses also intermarried with Roman patricians. That way, trough Constantinus Chlorus (father of Constantine) it went to the Merovingian dynasty... who have quite traceable descendants, if not line heirs. The other route were the vassal Greek kings, whom Rome allowed to maintain some power, and the kings of Armenia and Georgia. Plus, some Roman aristocracy survived in the Byzantine Empire. They married daughters of and gave daughters in marriage to European families, especially those active in the crusades. Also, marriages with Hungarian and Valachian houses were quite common, and some with Russia. There was even a Polish line of the Byzantine Imperial house of Lascaris (Lascorz in Spain is the same family).

Yet another way would be through Vandal kings who were related to Roman Emperors and whose daughter is the ancestor of those semi-legendary Scandinavian kings, including Rurik whose offspring was literally all over Russia and territories held by Lithuania and Poland.

See... it goes from Emperors to Kings, then to lords, until even simple knights, sometimes. It can go back the same way as well. This way, just about everyone who is related to some noble is related to some ancient kings and can prove that through historical records. It goes back and forth and even if one line is not really true (ie false genealogy, adultery of the wife etc), there are other ties leading to the same ancestors at some end.

So it's not really all that exceptional (more or less everyone is related to everyone), though still looks impressive :D