I always feel a little like Marty McFly when I listen to old-time radio shows on my iPod or computer. Here are several websites that give free downloads and/or streaming of a variety of programs:
Wizzard Radio hosts about 85 different podcasts relating to old Radio Broadcasts including:
My favorites are the Agatha Christie Radio Mysteries. Unfortunately, the site no longer produces new feeds, but you can still download old episodes from the website.