The Habsburgs got freakishly inbred for awhile there, routinely marrying uncle to niece and double first cousins to each other. Part of it was a desire to keep certain lands in the family, and part of it was a lack of other Catholic dynasties of equivalent rank to marry with – so the Habsburgs tended to marry other Habsburgs. The notoriously inbred and pathetic Carlos II of Spain, physically and mentally deficient, is the most famous result of this, but astonishingly Carlos II had a full-sister, Margarita Teresa, who married their uncle and produced a surviving daughter of her own, Maria Antonia.
Maria Antonia of Austria, the aforementioned niece of Carlos II, may be the most inbred European royal in recent-ish history of whom we have good documentation. Most people have 31 great-great-grandparents; Maria Antonia had only ten unique great-great-grandparents, and all of those ancestors were all closely related to one another. She was decended from her great-great-grandparents, Archduke Charles II of Austria and his wife Maria Anna of Bavaria (who were uncle and niece themselves), three times.
Somewhat less famously, the Chinggisids (descendants of Genghis Khan) also tightly intermarried. Although the khans took many wives and concubines, their successors were almost always the sons of their chief wife, who was usually very closely related to them. They often married nieces and cousins, and even weirder, when a khan died his concubines would be inherited by his sons or brothers. This sometimes resulted in messes like that of Kokaji, a concubine to three Il-Khans of Persia in succession (Arghun, his brother Ghaykhatu, and Arghun’s son Ghazan) and had children by all three of them.
Hulagu Khan’s daughter Todogach married Tanggis, khan of the Oirats, then after his death married Tanggis’ son Sulamish, and after his death married Sulamish’s son Chechak. So she was married to grandfather, son, and grandson. It gets weirder. Todogach and Sulamish had a daughter, Oljatai, who married Arghun, Il-Khan of Persia (who’s father, Abaka, was a son of Hulagu). Another of Arghun’s wives was Kutlug, daughter of Tanggis by his other wife, a daughter of Guyuk Khan (himself son of Ogodei). Kutlug was the mother of Ghazan, Il-Khan of Persia. Hulagu and Guyuk’s fathers, Tolui and Ogodei respectively, were brothers and sons of Genghis Khan. Is your head spinning yet?