Smodcast, iFanboy, the Savage Love Podcast, and Rachel Maddow. None of these have anything to do with gaming.
What I'd like to talk real briefly about tonight is the greatness of the Role Playing Public Radio, or RPPR podcast. I first discovered RPPR a little over two years ago, right when they were starting out. The hosts, Tom and Ross, have fantastic chemistry. Yes, there is swearing, and yes, internet memes do often rear their ugly viral heads from time to time, but they never stray far from their topic, and I really appreciate the actual content from these guys.
The regular format for their show is for the guys to pick a topic to discuss related to tabletop RPG's and then go into a more free-format shout-out/"letter from Tom" section. The topics they pick are really nice in that they rarely are applicable to only game system. From time-to-time they do focus on specific genres, and their insight into the horror genre specifically is enlightening, but still it's more theory based than running any specific scenario or campaign. These guys have a lot of experience in gaming - both positive and negative - and have tons of great anecdotes for examples of what they're talking about.
The two other major highlights are their extensive catalog of "actual play" podcasts (podcasts that are live recordings of real play sessions) and their free D&D 4e campaign setting "The New World" (of which there are many actual play sessions recorded as well). Their group is very entertaining for their actual play podcasts and you get a lot of bang for your download since they are epically-long times for a podcast (most podcasts don't tend to go for 4+ hours!). There are a lot of gaming podcasts out there, including some I may discuss in the future, but RPPR's my favorite. They're reliable, and always insightful. They stay on topic, and the hosts don't ever annoy, both of these features are unfortunately quite rare among the genre of podcasts. Go give 'em a listen, and you won't be disappointed.