COOP made blog post celebrating Don Mossi, a quite unusual-looking fellow who played professional baseball from 1954 to 1965. Apparently, he was nicknamed "The Sphinx" and "Ears." As Mark F. said, he'd have been a great character actor. From Wikipedia, here is what baseball historian Bill James said about Mossi:
"Don Mossi was the complete five-tool ugly player. He could run ugly, hit ugly, throw ugly, field ugly and ugly for power. He was ugly to all fields. He could ugly behind the runner as well as anybody, and you talk about pressure … man, you never saw a player who was uglier in the clutch."