Is there a rule that it’s illegal to post links to podcasts?
Anyway, I don’t know if this one will make sense to anyone outside of Australia, but I compulsively listen to a little program here called All Over The Shop - a very funny look at the week in news, in culture, in beer, in whatever. All the music is cut out of the podcast (for copyright reasons), so the two hour show is generally cut to around 50 minutes.
The two anime podcasts I listen to are Anime Pulse and my favorite, Anime World Order. I prefer the latter because the hosts are bitter and snarky and like old anime shows like I do.
I also like Coffee Break French and Radio 360, which has the kind of music that only gets played on NPR, if at all.
Rather ironically*, I discovered Hardcore History looking for James Burke related things (Dan Carlin interviews Burke on one episode). I’ve only listened to a few but they’re pretty good.
*For the unitiated: Connections
Leo Laporte’s got about 15 podcasts. I listen to TWiT, MacBreak Weekly, FLOSS Weekly, Windows Weekly, Daily GizWiz, and MunchCast.
Other podcasts that I listen to are:
Future Tense
Archeaology Channel
BBC Focus Magazine
BBC History Magazine
Center for Strategic and International Studies
Council on Foreign Relations
Cities of the Future
Classic Tales
Classical Mythology
ConceptMOTO <video podcast>
Digital Planet
The Discovery Files
Dr Karl and the Naked Scientist
Engineering Innovation from the National Academy of Engineering
Engines of Our Ingenuity
Great Books
The History Network
The History of Rome
I Should be Writing 2.0
Inside Renewable Energy
Le Show (Harry Shearer’s show)
LibraVox Audiobooks
Make Magazine <video podcast>
More Hip Than Hippie
Nature
NOAA, Ocean Explorer <video podcast>
Nova/PBS
Old Time Radio Sci-Fi
Point of Inquiry
PRI’s The World: Technology
Science in Action
Science Magazine
Science Talk: The Podcast of Scientific American
Science Times
Science Update
Science Weekly
The Scientist
Slice of Sci-Fi
Steampunk Spectacular
Steampod
Stone Pages Archeao News
Engineering Works
UChannel Podcast
United Nations Radio Features
The Ungodly Hour
WhiskyCast
And damned near every one of NASA’s podcasts.
I was going to recommend Skeptoid as well. That’s my favorite podcast.
I also like NPR’s podcasts.
I like Dr. Bob Price’s “The Bible Geek” and Reggie Finley’s the “Infidel Guy Show”.
PBS has some good ones (NOVA Vodcast).
When reading this list I thought one of the first podcasts listed would be CBC’s Quirks and Quarks This is an hour long weekly radio show with indepth articles about what is making news in the science world. I save them up and listen to them on long drives. http://www.cbc.ca/quirks/
Escape Pod (SF stories - some new, some classics). And its spinoff PodCastle (fantasy); there is also a horror spinoff PseudoPod that I don’t listen to.
This American Life of course, it’d be un-American to miss it, right?
X Minus One - rebroadcasts of 50s radio dramas based on SF stories.
Decoder Ring Theatre - new radio dramas in the style of 1940s radio serials (their big character is The Red Panda, a Batman-like character in Toronto).
Atlanta Radio Theatre Company - more radio drama. A wide variety of topics - I remember an HG Wells story, some SF, and other sorts of stuff… That one is a bit more sporadic than some.
LSAT Logic in Everyday Life - Applies the logic of the LSAT (Law School Admission Test) to everyday events in the news, politics, advertising, and conventional wisdom. Good for the non-lawyer.
Occasionally, I’ll download *The Mike O’Meara Show *(nee The Don and Mike Show) pod-casts. I generally listen to the show for the entire 15 minute commute home, so if the show seems like a keeper, I’ll snag it and listen to the full version in the morning.
I’d like to listen to Bob and Tom Show podcasts, but they make you subscribe (like $15 a month or something) in order to get them.
I listen to The Skeptics’ Guide to the Universe. I am pretty sure Rebecca (one of the panelists) frequents this SDMB because she’s mentioned it in the podcast in the past.
I’ve added quite a few of the ones mentioned in this thread. Before this, I had only two:** Stephen Fry’s Podgrams**, which originally alternated between unstructured ramble/rants and more formal monologues, and as of his most recent epistle seem to have went video; and Akira the Don’s Doncasts, which have served as a perfect way to be exposed to an eclectic mix of music, as well as whatever AK Donovan’s been doing himself. AtD introduced me to The Indelicates, and Stephen Fry has convinced me to look into Oscar Wilde’s fairy tales.
How are the steampunk ones? What’s the format/content?
Off the top of my head, I listen to:
TWiT
Macbreak Weekly
Cnet Buzz Out Loud
Savage Love
Economist
BBC World
You Look Nice Today
gdgt
On the Real With Chuck D
Marketplace
Diggnation
Disciplined Investor
Car Talk
Skeptics Guide to the Universe
This American Life
Cool, many things to go check out. The only thing I listen to regularly is about video games, the Giant Bombcast.
Steampod is readings of steampunk short stories. Steampunk Spectacular is sort of a hodge podge. They have interviews with folks in the steampunk community, movie/book reviews, and terminology discussions. Its a bit “cutesy” at times (for example, they talk about some of the things as if they were real, rather than just nerdy ideas), and they haven’t posted any new episodes in a couple of months, but the ones they have up are worth listening to, IMHO.
cool…thanks. I’ll check them out…don’t know why i never thought of looking for a steampunk one before. Kind of like when I never realized to even check if language education podcasts exited, which seems completely obvious in retrospect…
I’m a big fan of Keith and the Girl, a funny daily hour-long talkshow that features stand-up comedians as guests.
I also can’t help but like the Sick and Wrong podcast, infantile as it may be.
I share some favorites with others here: Wait, Wait Don’t Tell Me and Car Talk.
And I have a whole bunch of computer programming related shows I like to listen to.
I’m quite fond of Astronomy Cast. The hosts are Dr. Pamela Gay, an astronomer, and Fraser Cain, the publisher of an astronomy webzine called Universe Today. They do a half hour show each week; they often do a second episode dedicated to answering listeners’ questions.
I’ve been beaten to most of my suggestions, but may I add -
CBC’s The Vinyl Cafe
Lars Brownworth’s 12 Byzantine Emperors
Returning to add Hidden Kitchens. I used to listen to it on the radio, back when my job involved fairly extensive driving, and recently found it again on Stitcher on my iPhone. As an almost-foodie*, I find the exploration of our relationship to food and cooking fascinating.
*Perhaps a foodie-to be, or a foodie at heart, pending income and relocation. 
Groovelectric and Podrunner.