Here are FOUR very good sites for broadcast radio - old and new.
http://www.radiolovers.com/ is a free site offering thousands of classic radio programs from the 30s,40s, 50s, and although there is a fee
http://www.rusc.com offers an even greater selection of classic radio. You literally have 20 thousand hours of radio at these two classic braoadcast sites. The good part about having TWO sources of classic broadcast is that you will find some "missing broadcasts" on one site at the other site and visa-versa.
http://www.shoutcast.com/ is a streaming collection of thosands of live internet radio, mostly commercial free and at all bitrates and finally
http://www.scifi.com/pulp/set/set_classics.html which is the Sci/Fi Channel on TVs site with Modern made radio theatre including many selections from tales from the Crypt.
Great radio is a book for your ears - I'll sit back and listen to these over half the crap on TV any day - and NO I'm not an old fart either, I just have good taste

It's interesting to hear the Old Sci-Fi programs from the 1930s and 40s talking about "Way in the Future in the year 2000" We have a very different world then what it was THOUGHT to be like back then - nope, the Martians and houver crafts are circling the globe (yet) but CGI magic makes it so realistic that you swear they are.
The one thing that totally amazes me, there was LOTS of talk about computers and what they would do and couldn't do - but I have NEVER heard a sci-fi show YET that explained the INTERNET anywhere close to the impact that it has on every day life. No one saw the communication age coming, as NO ONE ever sees ANY AGE coming - makes you wonder WHAT AGE is coming next!!!!!
Give all these sites a try, you'll like them I'm sure.