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Here are a few I like:
http://www.slate.com/articles/podcasts/gist.html Daily news done with attitude
http://themoth.org/ story telling
The following are bike related:
http://www.thepodcasthost.com/thesprocketpodcast/ from Portland, biking, beer and simplifying
http://www.mprnews.org/topic/pedal-hub/ 3 MN bikers chatting
http://streetsblog.libsyn.com/ urban transportation issues around the country
Favorite is definitely WTF with Marc Maron (http://wtfpod.com)
Others: Radiolab, Shows on Earwolf (for instance http://www.earwolf.com/show/how-did-this-get-made/), This American Life
and although not really a podcast StoryCorps.org is wonderful to listen to.
Serial. (Most listened to podcast in history. There is a reason for this).
I also have a hardcore obsession with the NFL, so I can recommend NFL specific podcasts to anyone who who wants to listen to jocks talking about jock stuff.
NPR shows as podcasts:
Intelligence squared debates
On the Media
Wait Wait Don't Tell Me
This American Life
The Great War is more of a Youtube Series that, week by week covers WWI and what happened 100 years ago that week. An episode a week for the next couple years. I'm juuuuust about caught up at the moment and I'll bee current (+100 years)
If you want you can use a converter to turn a YouTube to an MP3 and listen to it as audio on the move.
Futility Closet. That's the only one I have time for.
Oh...also found this one when I was riding across the country.
Stuff you missed in history class
I LOVE podcasts. I don't even remember how I functioned before them. Here is my list -
1) The pop hits - TAL, Radiolab
2) Invisibilia. Reminds me of early Radiolab.
3) Ask Me Another. NPR quiz show that's much more up to date in its humor than Wait Wait Don't Tell Me (could they make ANY more jokes about twerking and selfies?). Lots of trivia and puzzles!
4) Planet Money. This podcast once convinced me I wanted to go to graduate school for economics because of how fun its discussion of economics is. I shouldn't do that at all
5) How To Do Everything. Always makes me chuckle
Also, I think I am the only person who doesn't like Maron or Dan Carlin. Everyone else seems to be super into them but I get so bored.
Cool topic. I'm a total podcast newb. Just subscribed to that 99% Invisible.
I think I must be the only person in this country who can't stand Ira Glass and This American Life and therefore, hated Serial in so many ways, even though I stuck with it until the dreary end.
I'm really surprised Harry Shearer's "LeShow" isn't listed. I never miss that one.
What?! Nobody listens to Chicago's own Pie Factory Podcast?! I'm hurt. *sniff* :) (Did I mention I co-host that one? :) ) It's a biweekly podcast about retro arcade video games. Jim and I discuss two games, our memories, strategies, etc., and in the end we reveal the theme that the two games have in common. For example, our first episode discussed Donkey Kong and Donkey Kong 3, and the theme was games in which Donkey Kong was the antagonist. (Sometimes we get more obscure -- for one episode we discussed Frogger and Asteroids. The theme: games that I first played at Hunk's Pancake House in Bradley.)
My favorite podcasts:
Fab 4 Free 4 All -- a great Beatles podcast that's even fun to listen to when the topic isn't of interest
Serial -- because Serial
Undisclosed -- because Serial
Atari 2600 Game By Game Podcast -- because I'm a retro gaming nerd
Atari 7800 Game By Game Podcast -- again, the nerd thing
And like many people here, I listen to Wait Wait! Don't Tell Me! and its sister podcast How To Do Everything. Used to listen to 2600's Off The Hook (actually a weekly radio show but available in podcast form) but I kind of grew weary of it. Still read their magazine religiously though.