In the early 1800s, the Fugate family (better known as the “Blue” Fugates) lived in the hills of Kentucky… and many of them were blue. Some of the family members possessed a hereditary genetic error called methemoglobinemia, which causes the blood to have reduced oxygen levels. With lower oxygen levels, arterial blood that is typically red is instead brown. In Caucasians, brown blood gives the skin a bluish hue.
I doubt the Fugates, though blue, even make it into the top 10 freakiest hereditary mutations to come out of the hills of Kentucky.