Here are links to some sites where you can find old time radio dramas.  Some of the sites offer a choice of listening or downloading.  The files are quite large (3-10 Mbytes).

You will need a player.  The files will be Real Audio (.ra or .ram) or MP3.  If you don't already have a player, I can recommend Winamp.  It will play either type of file and it is free.  There are a number of other players and most are free. 



Here are a few links:

Contains only The Shadow, Doc Savage and The Avengers.
This one has only one Shadow episode that changes weekly.
This has become a subscription site except for a few freebies.  However, the subscription is very reasonable and the selection is huge.  For about $5.00 you can download more than 90 half-hour shows and there are thousands to choose from.