For the past few years I've been falling asleep listening to an old iPhone 4 tucked under my pillow with the volume at it's lowest level. No earphones are necessary and my wife doesn't even realize I'm doing it.
I don't listen to podcasts but dialog-heavy movies that I've seen many times. I have a list of about 2 dozen movies that I go through depending on my mood, but they're all relatively quite without much action, just pleasant material. Since I've seen the movies it's easy to visualize along to the dialog and sleep comes (relatively) easy.
That having been said, the white noise of a fan is always lovely to fall asleep to.