American Archive of Public Broadcasting - historic programs of publicly funded radio and television from across the United States; you can facet by year after your initial search, but note that less than half of all records for digitized assets are currently dated, as cataloging is still in progress.
The Goldbergs on the Radio (UCLA Film & Television Archive) - Online access to a selection of the 130 episodes of The Goldbergs (1929-1946) preserved at UCLA.
The Museum of Broadcast Communications - To find digitized materials, select the "All Available Online Video" Collection
Old Time Radio Researchers Group - A community of "old time radio" enthusiasts catalogs and maintains a database of radio programs, scripts, magazines, and articles.
Radio Free Europe/Radio Liberty Records (Hoover Institution Library & Archives at Stanford University) - Broadcast and Corporate Records for the study of the Cold War the collection includes 10.5 million pages and more than 100,000 sound recordings from the 1950s to 2006. A selection of the collection is digitized and available in the "Radio & Television" section of their digital collections. Filter by date range for the appropriate time period.
British Entertainment History Project - "For the past thirty years, The British Entertainment History Project has been recording the stories of men and women working in the UK film, television, theatre, and radio industries to ensure that information on their lives and experiences is preserved for future generations."
Ronald Reagan Radio Commentary Sound Recordings (Hoover Institution Library & Archives at Stanford University)- A selection of digitized sound recordings from a larger collection of radio broadcasts with Ronald Reagan (late 1970s).
Studs Terkel Radio Archive - A growing online archive of more than 1,200 programs from Studs Terkel's 45 years on WFMT radio, broadcasts date 1953-1997.
Willis Conover Collection (University of North Texas Music Library) - Willis Conover (1920-1996) is best known for his 41-year career as a host of the program of Music USA on the Voice of America. The UNT Digital Library contains a small selection of program lists, recording schedules, and promos from the larger collection.