As my bitter rivals in the Archaeologists’ fitbit group (join us!) can attest, I usually walk a few miles a day. While I listen to a lot of music while I write, I let podcasts transport me across the landscape. They’re my television, I suppose. Back in 2010 I recommended a couple of Archaeology Podcasts, and the field has grown considerably since then, but I draw interest and inspiration from other topics.
So, my favorites:
New Yorker: Fiction – These are authors who have published in the New Yorker discussing the short stories of other authors. There is a long prelude and sometimes a long discussion afterwards that talk about the author’s life and the meaning of the story. These can sometimes grate, sadly. Still, I love reading the short stories in the New Yorker and the podcasts are a welcome jolt of incredibly good writing. They’re only uploaded once a month though, so I try to save it for a time when I can listen to it straight through on longer walks & bus rides.
AnthroPod – A newish podcast from the Society for Cultural Anthropologists with very pithy, involved conversations between anthropologists about their research. Particular favorite was John Hartigan on Race, Genomics, and Biology and Michael Fisch on Tokyo Commuter Train Suicides.
Thinking Allowed – A slightly quirky sociology podcast with Laurie Taylor that explores current research articles, generally bringing in the authors of the publications. Can be overly folksy and pseudo-populist, but I like the update about what is going on in one of our sister-disciplines.
This American Life – Yes, I am a member of the cult-like following of this show. For non-Americans, it has a lot of stories that are not necessarily American-specific. If I could only listen to one podcast, this would be it. Good thing there are over 500 episodes.
Radiolab – A broadly-conceived science podcast that follows interesting stories with odd resonance. They also do a lot of overtly reflexive audio editing, which you don’t see very often–compare with Jai Paul’s str8 outta mumbai. They broadcast a mix of in-depth hour-long podcasts with 20-30 minute “shorts” that can be less formal.
Fun stuff:
Escape Pod – Speculative fiction short stories of all stripes–so much so that sometimes they get complaints that the story isn’t actually Science Fiction. One example is The Paper Menagerie by Ken Liu, a lovely story steeped in Chinese culture about origami that comes to life. I’m often jealous of the stories, able to describe human interaction and possible realities better than any archaeologist or anthropologist I’ve ever read.
PodCastle – A companion podcast to Escape Pod that I only recently started listening to. The quality, to my ears, is a little bit mixed, but I enjoyed The Calendar of Saints, which is an incense-laden homage to Catholicism and a lady with a sword.
Friday Night Comedy – Dan and I like listening to this political comedy show while we’re cooking dinner. It is, in my opinion, a pale shadow of The Daily Show, but keeps me relatively up-to-date with British politics. May be slightly indecipherable if you don’t live in the UK.
Honorable mentions:
These are podcasts that I’ve downloaded with the intention of listening to them, but haven’t quite gotten to them, or have only listened to a couple of episodes: Welcome to Night Vale, On the Media, Material World, The Heritage Podcast, and From Our Own Correspondent.
Colleen Morgan 
I agree with a lot of these but need to include one more. ‘Science for the People’ formally called Skeptically Speaking. They have a new topic each week and bring in specialist to discuss different components of it. Tons of archaeology and anthropology related stuff in it.
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Heya Colleen (and heya Mary!). You should add TankRiot and KEXP’s Music that Matters to your list.
“The Memory Palace” by Nate DiMeo. Short bits of history. Excellently done.
Thanks for the Honorable Mention! Best wishes, Will (“The Heritage Podcast”)