I'll kick this off with an old-time radio program which is itself adapted from the short story medium. Broadcast on the series Escape in 1947, the tale is "Casting the Runes" by M.R. James, which you may recall ranked in my 100 favorite short stories. It also inspired the film Night of the Demon which has a following of its own (and is a good movie at that).
My old-time radio hobby was brought about thanks to local station QR77, which has broadcast old radio shows every evening for many, many years. I became an avid fan of old-time radio in my early teenage years in part because of the horror/mystery shows (although eventually I grew fond of all radio show genres). But after all, QR77's resources were only so great at the time. After a few years I felt that I had heard it all and there were few horror shows remaining that I hadn't heard and even fewer which would seem scary.
Then one night I heard "Casting the Runes." I had no idea what to expect and the show stunned me with its sense of dread. The story's protagonist is visited by a creature which follows him everywhere he goes. He can feel its presence, but never sees it. This fear of the unknown translated itself to the radio perfectly.
You can find a copy of the episode online here.