The son of acrobat parents, Morgan began his showbiz career as a child actor, including the role of Richie Petrie in Head of the Family, Carl Reiner's unsold 1960 pilot which would eventually be recast as The Dick Van Dyke Show. Shifting into juvenile and young adult roles, and often typecast as troubled teen or hoodlum, he appeared in Room 222, Bonanza, Ironside (with Raymond Burr), The Partridge Family, Happy Days, and the movies Wait Until Dark (1967, with Alan Arkin), Fuzz (1972), and most notably Logan's Run (1976). Keeping in type, he played Candlewick in a 1976 TV Pinocchio (starring Danny Kaye as Geppetto).
He had one of his larger film roles in Disney's Pete's Dragon (1977) as Grover (no relation), one of the villainous Gogans. Smaller Disney parts followed, in The North Avenue Irregulars (1979, as the bighaired head of a rock band) and The Devil and Max Devlin (1981, with Bill Cosby and Elliott Gould). In 1978, Morgan played the title role in Gould's comedy Matilda, wearing a suit as a boxing kangaroo. Not long after, he shifted to stuntwork primarily, some of which would again involve animal suits (a bear in The Great Outdoors with John Candy and yet another kangaroo in Storybook).
His stunt resume includes Cujo, 2010, Honey, I Blew Up the Kid, Army of Darkness, Bean (with Rowan Atkinson), and both Hook and the 2003 version of Peter Pan. He doubled for Martin Short in Three Fugitives (1989) and The Santa Clause 3: The Escape Clause (2006) and for Ricky Dean Logan in the second and third Back to the Future movies. On TV, he was a stunt Ferengi on an episode of Star Trek: The Next Generation and doubled for Shia LaBeouf in The Even Stevens Movie. In 2011, in addition to The Muppets, he performed stunts for The Artist.