There are two major types of birthmarks: vascular and pigmented. Vascular birthmarks, the result of a deformity of an artery, capillary or other blood vessel, are incurred astonishingly by 1 in ten children at birth. However, within the first year of life, these vascular aberrations then typically right themselves and disappear, with only a small fraction growing into a larger tumor.
There is no scientific evidence to support the idea that certain shapes of vascular or pigmented birthmarks correspond to some sort of personality, predictable behavior or other element of human nature. However, as with all things superstitious, that has not stopped some from believing in such things.
One of the more famous historical incidences of the intersection of birthmarks and crazy beliefs were the 17th century witch trials in Salem. Some accounts have been interpreted as signaling that authorities sought out and burned at the stake any woman who had the abnormality of a third nipple. Not a classical birthmark as such, but certainly in those days every inch of a woman's body was examined and anything out of the fair-skinned complexion norm was a due cause for irrational conviction.
As a literary device however, birthmarks rank right up there with villainous scars, bad guy glass eyes and various other visual cue indicators of a character's delineated nature. One of the most famous classical pieces of literature to mine this territory is Nathaniel Hawthorne's short story The Birthmark. The facial birthmark of a lead female character, Georgiana, become the cypher battle ground for nature vs. science, man vs. woman and much more.
Many critics look at the story and birthmark symbolism as an allegory for the fact that perfection can never be achieved by humans, and that any pursuit of such is mere folly. As such, the short story tracks back once again to the realm where any discussion of the symbolism of birthmarks truly belongs: superstition, not science.