If you like Twilight Zone or X-Files, turn out the lights and listen to episodes of (appropriately) Lights Out, Suspense, Escape, Inner Sanctum, and a few other notable series from the horror genre. There were other series, well-known and rare -- The Whistler, The Shadow, The Hall of Fantasy, The Hermit's Cave, etc -- but these are
my personal favs.
Lights was written by Arch Oboler, a playwright and occasional film director
(he made one of the earliest and best anti-nuke flicks, Five, in 1951) with a creepy voice (he hosts each episode) and a great talent for inspiring fear and claustrophobia. Although some of the shows are creaky, notably Cat Wife (late 30's), the tale of a bitchy broad who turns into a feline, others retain an ageless sense of eerieness, like Bathysphere, The Ghost in the Newsreel Negative, Rocket To Manhattan, and African Story. This guy was like a talented version of Ed Wood, creating a lot of atmosphere on a shoestring budget.
Suspense was a long-running series that frequently featured a lot of name talent, like Lucille Ball, Eve Arden, Vincent Price, Orson Welles, Agnes Moorehead, Mercedes McCambridge, and other masters of audio media. Source material dipped into classics by Poe, Lovecraft, Bierce, Wells, Conrad, et al.
Escape's gimmick was the title verb, each episode focusing on the hero trying to get out of a bad situation, be it an isolated kingdom of blind people out to make him one of them, or a gazillion marauding red ants. or Nazi bastards intent on destroying democracy.
Inner Sanctum was perhaps the campiest of the horror shows, with its devilish narrator and its obsession with all things funereal. One of my favorites has a corpse for a backseat driver. another has a woman (Anne Seymour) convinced that her husband is a vampire.