This "real life Shrek" was Maurice Tillet (1903 - 1954), a professional wrestler who had acromegaly, a rare disease that caused bones to grow uncontrollably and led to severe disfigurement:
In his twenties, he developed acromegaly, a rare disease that causes bones to grow wildly and uncontrollably. Soon his whole body was disfigured as a result. This led to much pain for Tillet as this gentle man was being called names, berated and forced to flee the place he loved so much.
Seeking a new identity to fit his chronic disfigurement, Tillet fled to America where he made a living on his appearance by becoming a professional wrestler, and was dubbed as the “freak ogre of the ring”. His villain persona (”the French Angel”) was an instant success with the crowds. Perhaps the highlight of his career was on August 1, 1944, when The French Angel defeated Steve “Crusher” Casey for the American Wrestling Association World championship.
http://www.pantherhouse.com/newshelton/for-five-minutes-can-you-not-be-yourself/ | Maurice Tillet [wiki] | More pic at WrestlingClassics - via reddit (Update 3/26/07: also at The Human Marvel)