This radio adaptation (by Howard Koch) of the 1898 H.G. Wells novel first aired as a Halloween episode of "The Mercury Theatre on the Air," on October 30, 1938. That, of course, was long before I was born. But it's very famous for having caused a lot of listeners to panic, as it involved fake news bulletins that people thought were real. Anyway, the audio is available for download online, at MercuryTheatre.info, among other sites. I've probably listened to it at some point, and I've always thought it was a neat little bit of history. And I've always liked the fact that it was directed and narrated by Orson Welles, because his last name is so similar to the name of the author.
Invasion from Mars, NPR
L.A. Theatre Works
This is a remake of the 1938 broadcast, which aired on public radio on October 31, 1994. (Reproductions of the new broadcast, such as the one linked to above, will call it "War of the Worlds," but in the audio it is introduced as "Invasion from Mars.") I quite liked it, and I still have it on audio tape, having recorded it off the radio when it aired. The performance was produced by L.A. Theatre works. It was directed by John deLancie, who was also a member of the cast. Other members of the cast included various "Star Trek" actors: Leonard Nimoy, Dwight Schultz, Wil Wheaton, Gates McFadden, Brent Spiner, Armin Shimerman, et al. A couple years later, Nimoy and de Lancie formed the group Alien Voices, along with other Star Trek actors, to make more audio dramas of science fiction novels. I'm not actually sure if I ever heard any of their other productions, but I may have. (Strangely, I've long remembered the "Invasion from Mars" broadcast being done under the Alien Voices name, which just goes to show how faulty my memory can be.)