Go to
http://archive.org/ and search for "oldtimeradio" -
http://www.archive.org/search.php?query=collection%3A%22oldtimeradio%2224 pages of results, with some repeats. Comedies, variety, suspense, SF, horror, hard-boiled detective, soaps, big-band music, etc.
[later - Ah. Clicking through the alphabet nav bar on
http://www.archive.org/details/oldtimeradio might be better, with no duplicates and sensible sort order. ]
"Dimension X" is probably one of the better-known SF series, with stories adapted from works by very familiar authors -
http://www.archive.org/details/OTRR_Dimension_X_SinglesAlso "X Minus 1" beginning on Page 1 (of 3) -
http://www.archive.org/details/XMinus1_AFor something a bit more corny, it's hard to beat "Planet Man" -
http://www.archive.org/details/OTRR_Planet_Man - in the "Great jumpin' Asteroids!" vein with plucky kids, evil overlord burdened with incompetent minions, a folksy sidekick mechanic, an elderly professor, monotone-voiced robots, the usual. 1950-52-ish.
Make that title
"The! Planet! Maaaan! ... Man ... Man ... Man ... Man""2000 Plus" looks promising too, but I've only listened to the first episode. -
http://www.archive.org/details/otr_2000PlusThere are a few collections of news stories which intrigues me, because back then it was breaking news and people had no clue how things would eventually turn out. Not "history" as we see it in hindsight. Check out
http://www.archive.org/details/WWII_News_1944 and
http://www.archive.org/details/WWII_News_1945 for D-Day, VE Day, and VJ Day items.