Martin Landau began his career playing a gunfighter in the third episode of The Twilight Zone, and a time-travelling astronaut in the sixth episode of The Outer Limits. Soon he was starring as master of disguise Rollin Hand on Mission: Impossible -- which ran from 1966 to 1973 -- and on Space: 1999, which ran from 1975 to 1977. At the age of 66 Landau finally won an Oscar for his portrayal of Bela Lugosi in Tim Burton's 1994 film Ed Wood. In 2012 Landau also provided the voice of the science teacher in Burton's Frankenweenie, and had an uncredited role in the director's 1999 movie Sleepy Hollow as one of the early victims of the headless horseman. Landau was also in the 1998 X-Files movie (playing the doctor who tips off Mulder that there's something suspicious in the morgue).
Slashdot reader schwit1 remembers that Landau began his career playing a sadistic henchman in Alfred Hitchcock's North by Northwest (who appears in the climactic final scene on Mt. Rushmore) -- and that Landau famously turned down the role of Mr. Spock on Star Trek.