There's quite a few podcasts out there dedicated short stories. Recently a couple of these stories captured my attention and imagination. The first was released on the podcast Starship Sofa. It's called "Shark God Versus Octopus God" by Jeff VanderMeer and was read by the wonderful Grant Stone. I especially loved Mr. Stone's lively kiwi accented narration. A very mythic and fun story about Dakuwaqa, the god of sharks, and his quest to become the god of the sea. Plus, it features a giant octopus god. :-)
The second was from the first episode of PodCastle, a fantasy story podcast from the people brought you EscapePod. It's called "Come Lady Death" by Peter S. Beagle, read by Paul S. Jenkins. It's a beautifully written piece about what happens when Death is invited to a party. Bittersweet with a fairy tale edge, it's a wonderful little story.