Good job cherrypicking one of the most genetically forgeted up instances of mideval European royal inbreeding. Also lets not forget that even still, muslim inbreeding is worse and always has been worse than just about anything seen in Europe.
-Henry VI had some kind of mental illness which left him near-catatonic for long periods. It may have been inherited from the French royals; Henry's French grandfather, Charles VI, was also mentally ill, sometimes claiming to be made of glass. Charles's madness led to a civil war, and a English invasion — Agincourt and Joan of Arc; Henry's madness led to the War of the Roses — two wars, one of which effectively purged the English royal line of madness by almost exterminating it. This shows that occasionally Real Life can be more sensible than fiction: most medieval kings had to be competent, or they got removed.
-The Habsburg dynasty of Austria, the Holy Roman Empire, Spain, and various states in Northern Italy was excessively inbred even by the standards of late medieval European royalty, with a tendency towards mental instability as well as a distinctive underbite known as the "Habsburg lip" that got more disfiguring in later generations. The Habsburgs felt that not marrying "ruling houses" was beneath them and were also devout Catholics, meaning that a large part of German and European families were off limits after the Reformation, unless their partners were ready to convert. To make matters worse, after the Habsburgs split into an Austrian and a Spanish main line after Charles V/Carlos I, the two branches of the family kept trading marriage partners in order to continue to be able to inherit each other's throne should one of them die out. Marrying into the Spanish House of Trastamara in the early 16th century had been a shrewd political move to expand the family's power but a poor choice for genetic health as the pre-Reconquista Spanish houses were already pretty inbred. Even by that low bar, the Trastamaras were noted for their history of oddballs, although the number of truly crazy family members may have been overstated by their enemies.
-Don Carlos, the rebellious son of Philip II, was insane to the point of being physically dangerous and would take swipes at passing servants with a knife.
-Ferdinand II's favourite occupation was rolling around in the bin.
-More on Charles II: He was so severely physically and mentally disabled (he had the "Habsburg Lip" to such an extent that he could not close his mouth; that's why his tongue is poking out) that his subjects nicknamed him "El Hechizado", "The Bewitched". According to the medical coroner, Charles' body "contained not a single drop of blood, his heart looked like the size of a grain of pepper, his lungs were corroded, his intestines were putrid and gangrenous, he had a single testicle which was as black as carbon and his head was full of water." The only non-Habsburg genes Charles had received in the last four generations were from his father's syphilis, which was at that point just throwing swamp water up a backed-up sewage line. Unsurprisingly, he closed the Habsburg chapter in Spain by not perpetuating his line (though his advisers tried to get an heir out of him).
-All Habsburg lines tended to lead back to "Juana la Loca", a.k.a. Queen Joanna the Mad of Aragon and Castille...over and over.
-Emperor Ferdinand I of Austria wasn't the head-choppy kind of crazy but he was definitely epileptic and had a hydrocephalus. His (rather euphemistic) honorific was "the Kindly" or "the Benign" (Ferdinand der Gütige in German). He gave exactly one coherent order during his entire reign: upon being told by his cook that he could not have Marillenknödel (a kind of Austrian sweet dumpling stuffed with whole apricots) for dessert because apricots were out of season, he famously said, "Ich bin der Kaiser und ich will Knödel!" ("I am the Emperor, and I want dumplings!"). After being told by his chancellor Metternich that the people outside the palace were carrying out a revolution (in 1848), his answer according to urban legend was: "Yes, but are they allowed to do that?" Since he remained childless, his disabilities did not continue down the line. Not that the line would ever have become Emperors; after the aforementioned revolution, the government convinced him to abdicate in favor of his saner and (it turns out) hypercompetent nephew Franz Joseph (who would reign until 1916).
