The following are links to recordings of some old time radio plays:

The Shadow and other free old time radio shows

Radio Yesterday (includes episodes of The Lone Ranger) 

The Lone Ranger Rides Again (7 best episodes in streaming real audio) 

Mercury Theatre (many from the '30's such as War of the Worlds, Treaure Island)   

Future Tales Radio Plays (many from the '50's) 

CBC Old Time Radio Plays CBC Mystery Theatre (samples only)

More information about radio plays here.

A webquest about radio plays that teaches you everything from the history of radio plays to how to make your own script and sound effects.

Resources used in the webquest that you may be interested in (courtesy Cynthia Matzat creator of Radio Days webquest)

Old-Time Radio: The Golden Years

The History of Radio

Any Year in History 

Format for a Radio Play Script

Vintage Radio Script Library Page 

1938 "War of the Worlds" Radio Broadcast Wavs 

Sound Effects  

The Art of Foley  

Movie Sound Effects  

Radio Sound Effects