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. Michael Constantine played Pollock. In the story line, a fledgling Denver copes with vandalism and the theft of turkeys, and Greeley is determined to report the truth about the emerging settlement.

Baer was Director of special events at KSL in the 1930s. 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 Benet'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.

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. He made six guest appearances on Perry Mason during the last five seasons of the CBS legal drama, including the role of Edward Farraday in the 1962 episode, "The Case of the Captain's Coins," and Willard Hupp in the 1963 episode, "The Case of the Bouncing Boomerang."

In 1952, he began playing Chester, the unofficial deputy to Marshal Matt Dillon on Gunsmoke, eventually ad-libbing the character's full name, "Chester Wesley Proudfoot". (The character's name was changed to "Chester Goode" in the television series, which featured an entirely different cast.) Baer's portrayal of Chester was generally considered his finest and most memorable role and, as he often said, the one he found most fulfilling. Baer worked on several other radio shows produced by Norman MacDonnell, including the situation comedy The Harold Peary Show (aka Honest Harold) as Pete the Marshal, Rogers of the Gazette (loosely based on the early life of Will Rogers) as Doc Clemens, Fort Laramie, and The Adventures of Philip Marlowe.

Baer's film roles included parts in several live action Disney features, including Follow Me, Boys! (again as a mayor), The Ugly Dachshund, and Those Calloways. He also appeared in Two on a Guillotine and Dave (as the Senate majority leader). Baer had a featured role in the 1958 war drama The Young Lions, portraying a German officer and friend of Marlon Brando.

In 1961, Baer guest-starred on Marilyn Maxwell's short-lived ABC drama series, Bus Stop. 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". He was cast as hotel owner Mr. Kringelein in the 1962 film, Gypsy, opposite Natalie Wood and Rosalind Russell.

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 made at least two appearances on Petticoat Junction. In the 1966 episode: "Jury at the Shady Rest", he was Bailiff Tucker. Then, in the 1969 episode: "The Glen Tinker Caper", he was Judge Madison.

In 1967, Baer appeared as General Whitfield on the I Dream of Jeannie episode, "Fly Me to the Moon".

In 1969, Baer gave the eulogy at the funeral of The Andy Griffith Show castmate Howard McNear. McNear had portrayed Mayberry's Floyd the Barber and Baer had played Mayor Roy Stoner. McNear also portrayed Doc Adams in the radio version of Gunsmoke, often interacting with Baer's character, Chester Proudfoot.

In 1964, Baer was cast as a sheriff in an episode of Mickey Rooney's short-lived Mickey sitcom, and as a scientist in an Outer Limits episode, "Behold, Eck!" He was seen in four episodes of Hogan's Heroes and eight episodes of Bewitched in various roles as advertising clients of McMann and Tate, including one Christmas episode entitled "Sisters at Heart" that aired on ABC on December 24, 1970 in which he played the role of Mr. Brockway, the owner of a toy Manufacturing firm.

Other recurring roles included Eb the farm hand on Granby's Green Acres (the radio predecessor to television's Green Acres), Gramps on The Truitts, and Rene the manservant on the radio version of The Count of Monte Cristo. 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.

As an on-camera performer, Baer was recognizable by his distinctive voice, his paunchy appearance, and his balding head. Often he portrayed fussy, bossy, and/or obstinate officials or neighbors. 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. He also appeared as a telephone executive on Gomer Pyle, U.S.M.C.

Baer voiced Ernie Keebler in the cookie commercials before he suffered a stroke in 1997 which affected both speech and movement. He recovered sufficiently to make a handful of appearances at old-time radio conventions in his later years.

In 1946, he met and married circus aerialist and bareback rider Ernestine Clarke. They were together for 54 years until her death on August 5, 2000, in Tarzana, California.

On November 11, 2002, following another stroke, Baer was taken to the Motion Picture & Television Country House and Hospital. Eleven days later, at the age of 88, he died there. Baer was survived by his daughters, Kim Baer and Dale Sloan, and three grandchildren.