[2] Despite dozens of appearances in television series and theatrical films, he remains best known as the original "Chester" in the radio version of Gunsmoke, and as the Mayor of Mayberry (Roy Stoner) in The Andy Griffith Show.

[2] Baer was commissioned as an officer in the United States Army Air Forces during World War II, attaining the rank of Captain.

[4] His first network show was The Whistler, which was soon followed by appearances on Escape (notably narrating "Wild Jack Rhett" and as the title patriot in an adaptation of Stephen Vincent Benét's "A Tooth for Paul Revere"), Suspense, Tales of the Texas Rangers (as various local sheriffs), Dragnet, The CBS Radio Workshop, Lux Radio Theater, The Six Shooter, and Yours Truly, Johnny Dollar, to name a few.

His later radio work included playing Reginald Duffield and Uncle Joe Finneman on the Focus on the Family series Adventures in Odyssey in the 1980s and 1990s.

Extended television roles included blustering, by-the-book Mayor Stoner on The Andy Griffith Show, the neighbor Darby on The Adventures of Ozzie and Harriet, frequent guest appearances on The Addams Family as insurance man and city commissioner Arthur J. Henson, and in the late 1990s, Miles Dugan on The Young and the Restless.

Baer guest-starred in the 1950s on NBC's The Dennis Day Show and It's a Great Life, on CBS's Hey, Jeannie!, on ABC's The Law and Mr. Jones with James Whitmore, on the syndicated crime drama Johnny Midnight with Edmond O'Brien, and on the NBC children's western series, Fury with Peter Graves and Bobby Diamond.

On April 13, 1962, he appeared, along with Frank Ferguson and Royal Dano in ABC's crime drama Target: The Corruptors in the episode "Journey into Mourning".

In 1963, Baer appeared with Charles Aidman and Karl Swenson in the three-part episode "Security Risk", a story of international blackmail and intrigue, on the CBS anthology series, GE True, hosted by Jack Webb.

Baer was cast as Horace Greeley, who came to Colorado in 1859 in the Pikes Peak Gold Rush, in the 1965 episode "The Great Turkey War" of the syndicated series, Death Valley Days.

Later guest appearances included Three for the Road, Three's Company (as a cooking competition judge), The San Pedro Beach Bums, The A-Team, Star Trek: Voyager, The Fresh Prince of Bel-Air, The Dukes of Hazzard, Night Court, Newhart, Little House on the Prairie, The Golden Girls, Hazel, and Mad About You.

Baer had a featured role in the 1958 war drama The Young Lions, portraying a German officer and friend of Marlon Brando.

[2][8] Baer was a long-term member of St. Nicholas Episcopal Church in Encino, California, where he served in many capacities, including head usher.