The Moth is a podcast of short stories told by amateurs, and a few professionals. They are told at a weekly event in New York or Los Angeles. People are selected to get up on stage and tell their stories, without notes, to the other story-tellers (the hardest audience).
You can listen to the Moth on their website or through iTunes. Nathan Furuya over at Kasai Gaidai recommended the podcast to me, and he is putting together of list of the best ones for teaching. I’ll share it with you when he gets it done. For now, they have a contest every once in a while, and here you can listen to the winners of the StorySlams.