What is a person who likes pain called?

A person who likes pain is called a masochist. Masochists enjoy situations that the majority of people would find painful or unpleasant.

In psychology, masochism often correlates with sadism and is referred to as sadomasochism. Once considered a mental disorder, sadomasochism is often expressed through sexual acts. Dr. Richard von Krafft-Ebing coined the terms in the 1800s, but historical records refer to the act of sadomasochism date back to the 1400s. In the 1990s, the American Psychiatric Association determined that sadist and masochist are considered mentally ill only if they forced their acts on non-consenting people or if their urges caused them distress.