Murphy began his comedy career as a performer on NBC's Saturday Night Live television show. His characters include a parody of Buckwheat from the Little Rascals and of Fred Rogers.
Murphy later starred in many comedies including the Beverly Hills Cop series and Coming to America. He is a versatile voice actor and voiced the donkey in Shrek and the dragon in Mulan.
Murphy had a one-hit wonder in the 1980s with the single "Party All the Time".