Historically, royal families have been fascinating tools for people interested in genetics and pedigree analysis; the combination of lots of inbreeding and the high profiles of the people involved allows one to assemble pedigrees of various interesting disorders that ran in these families.
It seems like most genetics courses cover the hemophilia pedigree of the descendents of Queen Victoria. However, there are some more interesting cases that I've never seen taught, such as the possible porphyria cases in the descendants of Mary, Queen of Scots and, of course, the infamous "Hapsburg lip" (or jaw).
The unofficial motto of the Hapsburg family was "Bella gerunt alii, tu, felix Austria, nubes!" ("Where others must fight wars, you, fortunate Austria, marry!). Due to the large amount of politically motivated intermarriage between Hapsburgs, the dynasty was virtually unparalleled in the degree of its inbreeding (when pedigrees look this recursive, all is not well). One particular phenotype that has been followed in this family is the mandibular prognathism and related traits (the "Hapsburg lip" or "Hapsburg jaw") first observed in Maximilian I (1459-1519).
As you can see from the pedigree, the trait was dominant (the heterozygous phenotype, however, appears to have been incompletely penetrant). The plethora of portraits of Hapsburg family members has allowed us to follow the trait through the generations--in fact, Albert Chudley was able to use postage stamps in his analysis of the Hapsburg jaw pedigree*.
The Hapsburg's intermarriage policy came back to bite them in the ass in 1665 when Charles II (the Bewitched) came to the Spanish throne. Not only did poor Charles have the most pronounced case of the Hapsburg jaw on record (his jaw was so deformed that he was unable to chew), he was also mentally retarded and impotent. He named Philip V of Anjou, a Bourbon relation, as his successor, which led to the War of the Spanish Succession at his death in 1700. The war ended Hapsburg hegemony in Spain and was the beginning of the end for the dynasty.
The Hapsburg jaw has been an interesting case for scholars over the years. Schroedinger mentions it in 1944's What is Life?, and James Watson (who has credited What is Life? with focusing his academic interests on genetcs) refers to it in DNA: The Secret of Life. It's always fun to look at these pedigrees and speculate about the role they played in history, though one suspects that people take them a bit too seriously (for example, I wouldn't try to claim that Alexis's hemophilia played a big role in the Russian Revolution).
*Chudley AE. Genetic landmarks through philately--the Habsburg jaw. (1998) Clin Genet. 54(4):283-4.