Like many nerds, I first encountered Paul and Storm at a Jonathan Coulton concert, and I was slightly annoyed at having to wait 45 minutes for Jonathan to take the stage—until they started talking. These guys won me over in moments; they are nerds to the core, interested in everything, and full of ridiculous stories. The podcast is usually just the two of them riffing on a couple of topics, and it's fascinating to hear two close friends and collaborators bouncing off each other.
The kitten rescue story in this episode made me laugh inappropriately on the train (I was sitting RIGHT NEXT to the door and garnered lots of strange looks at the Swarthmore stop): #117 That's One... (Bonus! Includes the afforementioned Jonathan Coulton!)
Are you in an argument with your roommate? Let John Hodgman decide your fate! With the brilliant Jesse Thorn as bailif, it's the best dispute-resolution show since Let's Bowl. Make sure to stand when Judge John Hodgman enters the courtroom.
Please explore all of the Maximum Fun podcasts. You can't go wrong, relying on Jesse Thorn's taste.
One favorite episode: #23 Arby's-tration
This podcast has a rotation of shows; my favorite is The News Quiz, which is what NPR based Wait, Wait...Don't Tell Me on. I've learned a surprising (and probably terribly skewed) bit about British politics from listening to the show. The BBC only keeps shows available for download for seven days, so don't forget to refresh your feed weekly.