Adams was heard on many radio programs during Radio's Golden Age. A notable recurring role was that of Pepper Young in Pepper Young's Family, which aired from 1947 to 1959. He also portrayed the deadly Nazi Atom Man in a classic 1945 serial on the radio version of The Adventures of Superman.

During the 1960s, he was ubiquitous as a voiceover actor in television commercials for foods and household products, most notably for Chiffon margarine and Crest toothpaste ("Helps stop cavities before they start"). He also did the vocal part of the television commercials for Smucker's preserves ("With a name like Smucker's, it has to be good!"), a role he resumed in his later years. Beginning in the 1980s, Adams provided the voiceover for Cadbury Creme eggs, which were advertised on television with Adams' catchy slogan, "Nobunny knows Easter better than him [the Cadbury Bunny]." Also in the 1980s, Adams did voice-over TV commercials for Sherwin-Williams Paints. Adams also did radio commercials for the Salvation Army. In addition, Adams was the narrator for Kix commercials in the 1990s as well as a few Dentyne commercials and a few Swanson commercials. He was also the announcer for a 1992 WCBS-TV news promo, as well as a 1986 Lysol commercial. In the early 1990s, he narrated The Discovery Channel series on milestones of aviation called "Frontiers of Flight". In one of the early episodes of Sesame Street, he voiced a cartoon featuring a "jazzy" triangle and a "square" square. He voiced those two, as well as being the narrator, with jazz music in the background. This cartoon was repeated on the show for many years, well into the 1980s.

During the 1970s, he was a co-star of the NBC soap opera Another World. In 1986, he starred as Col. Edward Mason, one of his most famous feature film roles, in the movie F/X starring Bryan Brown and Brian Dennehy, and appeared in the 1991 action movie Toy Soldiers. In 1993, he starred as Walter Warner Sr. in the movie Son in Law starring Pauly Shore, and his later film credits included roles in Houseguest (1995), Touch (1997) and The Lesser Evil (1998). In the 1998 HBO miniseries From the Earth to the Moon he played Senator Clinton P. Anderson. His final appearance in TV and Film was in the series finale of Oz.

He was also in the original 1976 Broadway cast for Checking Out. In 1983, Adams joined The Mirror Theater Ltd's Mirror Repertory Company for their first repertory season, appearing in Paradise Lost, Rain, Inheritors, and The Hasty Heart. This season was presented initially Off-Off-Broadway at The Real Stage Acting School and was moved Off-Broadway to the Theatre at St. Peter's Church.

Adams is perhaps most famous for his role as Managing Editor Charlie Hume in the television series Lou Grant, which aired from 1977 to 1982. During his run on Lou Grant, Adams performed perhaps his most often seen role, as the US President in Omen III: The Final Conflict (1981). He also appeared in popular TV movies, such as The Deadliest Season (1977), Revenge of the Stepford Wives (1980), The Kid with the Broken Halo (1982) and The Night They Saved Christmas (1984).

Adams married Margot Fineberg in 1958. The couple had a daughter, Betsy, and a son, Bill. He died on April 26, 2005, from natural causes, according to his daughter.

Adams was born in Brooklyn, New York. He earned an MA degree from the University of Michigan in Theatre Arts and Speech and also attended the University of Wisconsin–Madison, studying theater arts. He made his stage debut in 1940, appearing in summer stock at Baltimore's Hilltop Theater.