The Prelinger Archives at Archive.org
View and download many historical films, including those featuring radio history.
The Mercury Theatre on the Air
From the site: "The finest radio drama of the 1930's was The Mercury Theatre on the Air, a show featuring the acclaimed New York drama company founded by Orson Welles and John Houseman. In its brief run, it featured an impressive array of talents, including Agnes Moorehead, Bernard Herrman, and George Coulouris. The show is famous for its notorious War of the Worlds broadcast, but the other shows in the series are relatively unknown. This site has many of the surviving shows, and will eventually have all of them."

Free Old Time Radio Broadcasts
This site features many of the earliest and most obscure radio shows free to listen and download in MP3 format. Shows include: Hopalong Cassidy, Gunsmoke, Benny Goodman and Amos & Andy.
Radio Nostalgia Network
Features old time radio broadcasts. You can also subscribe to the podcast on iTunes or Zune.
The Museum of Broadcast Communications: Radio Hall of Fame Inductees
Read about some of the biggest talents in radio, including Red Barber, the man who gave his name to the WFSU Broadcasting center address; 1600 Red Barber Plaza.