1. The New Yorker: Fiction: The New Yorker magazine presents this podcast, where contemporary authors select and read a short story from the magazine's archives. It's a fantastic way to discover both classic and contemporary literature.

2. Selected Shorts: Hosted by Symphony Space, this podcast features well-known actors and writers who perform classic and contemporary short stories. The stories are often recorded live at literary events.

3. The Moth: While The Moth primarily focuses on live storytelling, they occasionally feature short fiction pieces as well. The stories are shared by everyday people and offer a mix of humor, drama, and heartwarming tales.

4. LeVar Burton Reads: Hosted by the beloved LeVar Burton, this podcast features Burton narrating a diverse selection of short stories, often in the science fiction and fantasy genres.

5. Escape Pod: For science fiction enthusiasts, Escape Pod offers weekly episodes featuring narrated science fiction short stories. It's perfect for those who love speculative fiction.

6. The Classic Tales Podcast: B.J. Harrison narrates classic literature, including short stories, with a focus on public domain works. If you enjoy timeless classics, this podcast is a treasure trove.

7. Lightspeed Magazine Podcast: Lightspeed Magazine specializes in science fiction and fantasy. Their podcast features narrated short stories and author interviews, providing an in-depth look at the genre.

8. Podcastle: As part of the Escape Artists family of podcasts, PodCastle focuses on fantasy fiction. They provide a wide range of narrated fantasy short stories and flash fiction.

9. Clarkesworld Magazine: Clarkesworld is a Hugo and World Fantasy Award-winning science fiction and fantasy magazine. Their podcast offers audio versions of the stories they publish.

10. The Drabblecast: This podcast specializes in weird, offbeat, and humorous speculative fiction. The stories are often quirky and unconventional.

These podcasts and platforms offer a rich array of narrated short stories across different genres and styles. Whether you're a fan of classic literature, contemporary fiction, science fiction, or fantasy, there's a podcast to suit your preferences. They provide an engaging and convenient way to enjoy short fiction, making it easier to fit reading into your busy schedule.