SF&F has a long history of short stories and magazines presenting serial fiction. I can't remember exactly what serendipity of the internet led me to the PodCastle.
http://podcastle.organd the sister podcast http://escapepod.org/ present fantasy and Science Fiction short stories read in podcast format. I'm late to the party, since there are 291 episodes on PodCastle before this one (and more than 400 on EscapePod). The episodes are a mixture of stories published in other venues and original fiction.
The second episode I listened to was "Seasonal Disorder" an original tale commissioned for the holiday season. It featured a showdown between the Snow Queen and the Sun King and in half an hour of driving I was charmed.
As with any anthology of short stories, I expect that the quality will vary. But I guess I've got a lot of listening to to do catch up to find the good ones. Too bad they won't count towards my books read for the year