I have found a group of podcasts which are weekly short stories in 3 main categories. Horror, Sci Fi, and Fantasy are how these 3 sister shows are divided. All are free and have a new story every week. These are some of the best stories I have heard. They can be listened to on their web sites, or subscribed to through itunes or their respective web sites.

Pseudopod is the horror podcast hosted by the chilling Ben Phillips. This is my favorite of the 3, although I really like them all. This is not some weekly slasher fest. No it is very well written stories covering the full range of horror. I have a story to tell you, and I promise you it's true.
http://pseudopod.org/

Escape Pod is the sci fi podcast, hosted by the far out Steve Eley. What can I say? Another collection of great stories set in the sci fi genre. I highly recommend Aliens want our women. It really makes you think about how the minds of our fabulous gals works.
http://escapepod.org/

Podcastle is the newest show of this trilogy, hosted by the  dreamy Rachel Swirsky. It just launched a month ago and covers the fantasy realm. The stories they have so far are incredible. It amazes me sometimes that content like this is given away for free.
http://podcastle.org/

And for you authors out there, all 3 shows buy their stories from the authors. And not just established authors, but any author. They all have open submissions on their sites. And if they like your story, they will pay you for it and read it on the show.