I've been listening to various podcasts for almost eight years now. A lot have come and gone, but my two long-time favorites are:
Escape Pod - Weekly short-form science fiction. These guys have been around since almost the beginning of podcasting. This is their sci-fi show. They also have horror (Pseudopod) and fantasy (Podcastle) among others.
StarShipSofa - Also weekly short-form sci-fi but more than just stories. This is an audio magazine with regular articles about science news (Delivered by a biology professor), genre history (Delivered by a history professor), interviews and more. It's part of the District of Wonders (Which also has horror, fantasy, and used to have pulp and crime before those shows withered away).
More recently I've been listening to these and getting a lot of interesting thought topics out of them.
The Skeptic's Guide to the Universe - Skeptical thinking, science news of all types (Astro physics, biology, technology, etc), interviews, and more. This one usually runs a bit long.
You Are Not So Smart - Psychology deep dives into various topics (logical fallacies, changing people's minds, detecting bullshit, etc).