Berg learned theater in college while simultaneously producing skits for her father's Catskills Mountains resort and married Lewis Berg in 1918. It was one of those skits, portraying a semi-autobiographical Jewish family in the New York tenements, that Berg soon developed into a fifteen-minute radio program. The Goldbergs became so popular---its plots and scenarios touching a chord with Americans of all stripe who identified with the situations even if they weren't urban lower-middle-class Jews trying to assimilate into the new world---that the show's characters received fan mail as often as the actors who played them did, and thousands of letters poured into the show's network when Berg herself was forced to miss time on the air due to illness.

Berg became inextricably identified as Molly Goldberg, the bighearted matriarch of her fictitious New York family who moved to Connecticut as symbolic of Jewish-American upward mobility. She wrote practically all the show's five thousand plus radio episodes plus a Broadway adaptation, Me and Molly, in 1948. It took considerable convincing, but Berg finally prevailed upon CBS to let her bring The Goldbergs to television in 1949, where it stayed in first-run production for five years. Berg herself won an Emmy award as Molly in 1949.

On television, The Goldbergs ran into trouble in 1951, when co-star Philip Loeb (as patriarch Jake Goldberg) was one of the performers named in Red Channels: The Report of Communist Influence in Radio and Television and blacklisted as a result. A strongly loyal person, Berg refused to fire Loeb. But Loeb was a strongly loyal man in his own right, loyal enough to Berg that he resigned rather than cause her trouble, and he reportedly received a generous severance from the show. It wasn't enough, however, to prevent Loeb from sinking into the depression that ultimately drove him to suicide.

The Goldbergs returned a year after Loeb departed the show and continued its first-run production until 1954, during which time Berg also wrote a film version of the show. The show remained in syndicated reruns for another few years, after one year of production under the title Molly. Most likely, the increasing homogenisation of television depictions of family life left little room for such an overtly ethnic show, however universal many of the themes explored in The Goldbergs were.

In 1959, Berg won a Tony Award as "Best Actress in a Play" for her performance in "A Majority of One." In 1961 she won the Sarah Siddons Award for her work in Chicago theatre. Berg also published a best-selling memoir, Molly and Me, in the 1960s, before she died of heart failure during routine tests in a New York hospital in 1966. A creative and energetic woman, Berg was among the earliest examples that women in broadcasting and on the stage could make themselves whole creative forces and not just actresses.