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."