Curtis made his film debut in the 1948 Orson Welles adaptation of Macbeth. Additional film credits included American Hot Wax, Rabbit Test, The Buddy System, I.Q., Heaven Can Wait, Sliver, and Richie Rich's Christmas Wish.
Curtis' theatrical career began in 1955 as a Broadway stage manager. His first appearance as a performer was in a 1965 revival of You Can't Take It with You. In 1971, he was awarded the Tony Award for Best Featured Actor in a Musical for The Rothschilds. Additional Broadway credits included The Cherry Orchard, A Patriot for Me, Via Galactica, Annie, Night Watch (played Curtis Appleby in 1972 production) and La Cage aux Folles.
Curtis had a recurring role playing John Allen Hill, the owner of Melville's Restaurant in Cheers and as a wealthy snob on Amanda's. His many television credits include The Magician as quirky columnist Max Pomeroy opposite Bill Bixby, Gypsy and appearances on:
For the animated series SWAT Kats: The Radical Squadron, he voiced the character the Pastmaster. He also provided the voice of Grand Moff Tarkin for the first Star Wars radio drama, but may have been best known for voicing "Lord Balthazar" of The Smurfs from 1981-89.
He also used his voice talents for other cartoon shows including The Little Mermaid, The Dukes, The Scooby & Scrappy-Doo/Puppy Hour, Bill and Ted's Excellent Adventures, Trollkins, The Adventures of Don Coyote and Sancho Panda, The Greatest Adventure: Stories from the Bible, Denver, the Last Dinosaur, The Snorks, The Jetsons, Space Stars, Adventures from the Book of Virtues, The Herculoids, Fantastic Max, Paddington Bear, The Centurions, Kissyfur, Mother Goose and Grimm, The Hot Rod Dogs and Cool Car Cats and Bonkers.