Hesseman was born in Lebanon, Oregon, the son of Edna (née Forster) and George Henry Hesseman. His parents divorced when he was five, and he was raised by his mother and stepfather, a police officer. He graduated from Silverton High School in 1958. Hesseman attended the University of Oregon, and was later a founding member of the San Francisco-based improvisational comedy troupe The Committee with fellow actor David Ogden Stiers. Early in his acting career, he used the alias Don Sturdy, the name he also used as a radio DJ.
Under the alias of Don Sturdy, Hesseman made some television appearances, including one episode of Dragnet in 1968 in which he portrayed a hippie named Jesse Chaplin, the editor of an underground newspaper. In this Dragnet episode, his character was a panelist on a TV show opposite Sgt. Friday and Officer Gannon.
He played a bit part in two final-season episodes of The Andy Griffith Show. In the episode "Sam for Town Council," Hesseman has an exchange with Emmett Clark (Paul Hartman), who is running for town council against Sam Jones played by Ken Berry. Hesseman plays a character named Harry seen preparing fishing tackle outside a sporting goods store and complaining to Emmett how poor the fishing has been at a nearby fishing spot. Emmett promises to stock the pond with big perch in exchange for Harry's vote. Harry agrees and wears a campaign button supporting Emmett in the race. In the episode "Goober Goes to an Auto Show", Hesseman, also credited as Don Sturdy, plays the Counterboy, serving hot dogs and root beers to Goober and his old trade school rival Roy Swanson, played by Noam Pitlik. Hesseman made several appearances as Mr. Plager, a member of the group therapy ensemble on The Bob Newhart Show, who was later revealed to be gay. He became a playwright in the sixth season of the show, writing a play about the characters in the group. In several other episodes of the show, Hesseman's voice can be heard as a TV announcer. In 1969, he appeared uncredited with The Committee (though at the time using the name Don Sturdy) in several sketches on The Dick Cavett Show, and appeared in one sketch with guest Janis Joplin.
Hesseman is probably best known for his role as anti-disco disc jockey John "Dr. Johnny Fever" Caravella on the television sitcom WKRP in Cincinnati from 1978 to 1982, a role Hesseman prepared for by working as a DJ in San Francisco at KMPX-FM for several months. He was nominated for a Primetime Emmy Award for Outstanding Supporting Actor in a Comedy Series in 1980 and 1981 for his portrayal of Fever. In 1986, he was in the Disney cult classic Flight of the Navigator. He reprised the role in nine episodes of The New WKRP in Cincinnati, and also directed several episodes of the 1991-93 series revival.
Hesseman is also remembered for his role as teacher Charlie Moore on the ABC series Head of the Class from 1986 to 1990. He also played Sam Royer, the man who married Ann Romano (Bonnie Franklin) on One Day at a Time. In 1994, Hesseman introduced lost footage of Joplin in a documentary on Woodstock. He made two appearances on Saturday Night Live, one in which he paid tribute to, and told jokes about, the recently deceased John Belushi and the other in which he mooned President Ronald Reagan. NBC showed a picture of Reagan, and Hesseman mooned the president off camera. He also encouraged the viewing audience to moon the picture and send pictures in to NBC.
In 1995, Hesseman played the principal role of the Marquis de Sade in Quills at the Geffen Playhouse in Westwood, California, which included one scene in which he was fully naked. In 2001, Hesseman had a role on three episodes of That '70s Show. In 2006, he appeared in three episodes of the ABC television series Boston Legal, playing the unorthodox Judge Robert Thompson, as well as an episode of House. During his appearance as Judge Thompson, Hesseman paid homage to his role as a teacher in his earlier ABC series by hearing a court case while sitting atop the judge's bench, just as the character of Mr. Moore taught his class atop his desk. In 2007, he played The Chemist on HBO's John From Cincinnati. He has guest-starred as an announcer at a horse track on Psych, in the episode "And Down the Track Comes Murder". Hesseman guest-starred on the 2007 season premiere of NBC's ER, playing a man tripping on magic mushrooms who may or may not have been an orthopedic doctor from another hospital. Hesseman starred in The Sunshine Boys at the New Theatre Restaurant in Overland Park, Kansas, from September to November 2010. In February 2011, he had a guest role as Dr. Elliot D. Aden in the CSI: Crime Scene Investigation episode titled "Turn On, Tune In, Drop Dead" from season 11 (episode 16). Dr. Aden was head of Department of Defense project called Stonewall at W.L.V.U., which did research in fringe psychological concepts such as E.S.P. and out-of-body experiences.