I listen to a lot of podcasts. Mostly because of working an office job:
Horrible Night - They're a very funny group of people. They host a lot of different podcasts (with mostly the same hosts and similar content) but their most entertaining one, IMO, is the Night Force Action Report, especially the parts where they talk about game ideas (taking a somewhat absurd concept and running with it) or when they talk about Animal Crossing. Their finest moment has to be when they were discussing their idea for an Animal Crossing NPC game.
Co-Optional - Mostly because I like TotalBiscuit. They usually have some pretty good discussion here.
Gamers With Jobs - I only just started listening to this one, but I was rather impressed. It's by and for an older crowd than most of the podcasts out there, and I appreciate the more in-depth discussion that that brings, though they do end up being less funny than say the Horrible Night people as a result.
Space Game Junkie - Mostly because I really like space games. They spend most of their time actually playing games on this one, so the video feed is preferred, if you have time for it. Since I don't have the time to single-task watching a podcast, I stick to the audio-only version, only occasionally checking the video if something sounds particularly interesting.
As for non-gaming podcasts, I like This American Life, Tech Report, Anime World Order, and ANNCast.