Movies
* The Stalking Moon (1968) - as Sam Varner
* The Grasshopper (1970) - as Jack Harris
* The Other Side of the Mountain (1975) - as Leo
* The Last Married Couple in America (1980) - as John
* The Best Little Whorehouse in Texas (1982) - as Sheriff Ed Earl Dodd
* S.O.B. (1981) - as Director
* The Big Red One (1980) - as Captain
* A Little Sex (1982) - as Dr. Howard "H.B." Baker
* The Jewel of the Nile (1985) - as Omar
* Some Kind of Wonderful (1987) - as Keith
* Three Men and a Baby (1987) - as Peter
* The Naked Gun: From the Files of Police Squad! (1988) - as Chief
* The Naked Gun 2 1/2: The Smell of Fear (1991) - as Chief
* The Santa Clause (1994) - as Neil
* The Santa Clause 2 (2002) - as Neil
* The Santa Clause 3: The Escape Clause (2006) - as Neil
Television
* The Doctors (1969-1971) - as Dr. David
* The Bob Newhart Show (1972-1978) - as Bob Hartley
* Soap (1977-1981) - as Benson
* Empty Nest (1988-1995) - as Dr. Harry Weston
* The Golden Girls (1985-1992) - as Dr. Harry Weston
* The Golden Palace (1992) - as Dr. Harry Weston
This is just a partial list, and Mulligan appeared in many other projects throughout his career.
He was known for his comedic timing and ability to portray both serious and humorous characters. He was a highly respected actor and his performances continue to be enjoyed by many today.