I listen to these, mostly comedy based podcasts:
Comedy Bang Bang - Interview format but mostly improvised chat and comedy with people coming on to play characters. One of my favourites, there are some absolute classics. Features a lot of appearances by the following podcaster:
The Pod F. Tompkast - Paul F. Tompkin's podcast, mostly solo/long form improvised conversation directed at the listener, although he does get guests on, plays some of his sketches from live shows and also has a serial storyline where he'll perform his characters putting together "The Great Undiscovered Project". I really like this. It's a different style to most podcasts, with a piano accompanyment throughout by Eban Schletter.
How Did This Get Made? - Paul Sheer, Jason Mantzoukas and June Diane Raphael plus guests get together to talk about who ridiculous terrible movies are, like Gigli, Street Fighter, Judge Dredd, The Love Guru etc. Great chemistry between them all and lots of fun to listen to.
The Thrilling Adventure Hour - A podcast in the style of old-time radio plays, performed live by actors like Paul F. Tompkins, Paget Brewster, Nathan Fillion, Busy Phillips, and a bunch of other great comedians. Rotates between different stories - Sparks Nevada: Marshall on Mars (space western), Beyond Belief (Twilight Zone esque investigations by drunk socialites) and others. Really recommend this one.
Superego - Improvised sketches, updated infrequently and the first two "seasons" may no longer be available for free, but well worth checking out what you can of this. Really funny.
Welcome to Night Vale - A fictional news radio broadcast from a strange town with all sorts of weird goings on. Just started listening to this after I heard about it recently.
Nerdist Podcast - Interviews with all sorts of people, there's so many of them now that you could probably just pick and choose who you're interested in hearing. Hosted by Chris Hardwick, who's entertaining enough.
Nerdist Writer's Panel - Hosted by Ben Blacker of the Thrilling Adventure Hour, this is a pretty much Hollywood-focused panel about writing for television. Interesting just for the stories behind it all, not sure how it would help people over here in taking up TV-writing but it's good for the insight you'll get into American shows, anyway.
I should listen to more British podcasts.