One literature-featuring podcast I enjoy is
Read It And Weep. Although it does feature coverage of books, it also features reviews of movies and TV shows (such as one on
My Little Pony: Friendship Is Magic).
Although it's not a literature podcast, although it does feature stories, is
The Story Song Podcast. Each episode features one song that tells a story and they give an in-depth analysis of the song (the song itself, its chart history, and the artist).