The Habsburg Jaw
This genetic condition, also called prognathism, is connected to noble families. The Spanish House of Habsburg came to power during the mid-1400s and remained there until the mid-1700s, but during that time, there was quite a bit of inbreeding. Rather than marrying outside the family, the Habsburgs arranged close marriages to protect their interests. Unfortunately, their genetics paid the price. Their children started to show long, jutting lower jaws, with severe under-bites.
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The worst case of this was found in Charles II of Spain, who had an under bite so severe that he could not speak properly, could not chew, and had problems with drooling. (In addition, he was infertile and had cognitive disabilities: he learned to talk when he was 4, and to walk when he was 8.)
Even modern ancestors of this family show slight variations of this genetic problem, showing just how long-lasting the results of genetic mutations from incest can be.
Misshapen Skulls
If you look at many ancient Egyptian busts, you may notice that their heads look a little funny - in particular, they are often elongated in the back. This wasn't just a stylistic choice on the part of the artist; many Egyptian royalty actually had skulls shaped like that.
After all, Egyptian royal customs depended heavily upon incest. Brothers married sisters; mothers married sons; and cousins often married cousins. The result was that their skulls were often deformed, although it should be noted that most royalty wrapped their heads to obtain that particular deformed shape as they grew, as it was also a sought-after style. King Tut, for example, suffered from such a skull deformation, in addition to "a cleft palate, a club foot (as well as missing bones in his feet), and scoliosis."