Sonic Society is a great place for short stories, they have sci-fi, comedy, horror... you name it! You'll specially want to hear it for their fan made Firefly audio play Dark Wounds! This audio cinema at it's finest, with professional voice acting and sound effects! Like I said "MOVIES IN YOUR HEAD"!
Spaceship Radio is a podcast where they air an old sci-fi show called "X-1".
Escape Pod has lots of short sci-fi and fantasy stories, and their sister podcast Pseudopod deals with horror stories.
Podiobooks is a site that has several full audio novels. I really recommend Ancestor, The 7th Son... Actually, I love ALL of them! :P
Decoder Ring Theater has two audio shows, Red Panda, and Canadian superhero of the past, imagine Bat-Man in the 70's if it was actually cool! And Black Jack Justice, the only "gumshoe" show I not only like, but adore!
And of course, I can't forget Librivox, a site of public domain audio novels and short stories!