My interest in any given podcast tends to wax and wane according to a great number of odd and obscured factors. This list is not exhaustive, it's just exhaustive of the ones I can both remember and generate an opinion about. I will attempt to organize them according to how much I would recommend them.
I am not even going to try to organize them. The only order is in my own memory.
Oh God I Listen To So Many
No Such Thing as a Fish - Four Brits share wacky facts. Great for a laugh, surprisingly educational.
Futility Closet - It's like the Dollop, but wholesome and uplifting. Husband-and-wife duo provide historical oddities and lateral-thinking puzzles.
Overdue - Talking about books! A whole lot of books. Books you haven't read but have probably heard of. Good hosts, good energy, talkin' bout books.
Literature and History - Hey would you like to explore the Western literary canon in chronological order? Would you like it in the format of an easy-going but very, very in-depth lecture series? (How in-depth? Beowulf isn't scheduled until episode 104) I've gotten a new appreciation for classical myth through the series, and familiarized myself with works I'd either never studied or never heard of. Love it.
Old Gods of Appalachia - Contains 1) old gods 2) the Appalachians 3) sassy Scotts-Irish witches. It might as well have been made to pander directly to me. Fantastic atmospheric writing.
The Legendarium - Fantasy book podcast. Had a series where one host read through LotR for the first time which was fun, but it ends up being rather tame by my going. Not in-depth or out-there enough to keep my interest. EDIT LONG AFTER THE FACT: These guys did an episode where they interviewed the guy behind Sad Puppies and I got no time for that.
Good Friends of Jackson Elias - Talking shop about Call of Cthulhu. Pretty low-key and relaxing. Fills time.
Expounded Universe - Would you like to know precisely how terrible some of the Star Wars Expanded Universe novels are? This has you covered. Absolute goof-fest. (Turns out you can fix 90% of the EU by just writing Leia as if she's an experienced and competent diplomat but, spoilers, no one does.)
How We Roll - Huge Call of Cthulhu campaign stringing together a bunch of noteworthy scenarios. Only got to the second scenario due to poor audio quality and a general "eh 's whatever' quality to the whole thing.
The New Adventures of Nero Wolfe - It was 1950 so yes, Archie's attitudes towards women and his means of talking about them are not particularly forward thinking and in one case are directed towards the corpse du jour. That aside, this is a wonderful series with great character dynamics and acting. Having now read one of the books, I can say it nails it.
Film Reroll -The best use GURPS has yet seen. Famous movies go off the rails, hilarity ensues. Alien and Adventure Time are great places to check out.
Pretending to Be People - A Delta Green actual play, featuring three bumbling cops from the middle-of-fucking-nowhere, Missouri. My favorite long-form actual play by a gigantic margin. It's legitimately horrifying in a lot of places and goofy bullshit right where it needs to be. Double extra supreme bonus points for running a mythos game and never once using a proper name. Not once. Not even once. Infinite unbelievable extreme bonus points for running a Delta Green game where ROT13 gur cynlref ner nyy ba gur znetvaf bs gur npghny QT bcrengvba tbvat ba va gur onpxtebhaq.
Magnus Archives - My opinion on this series is well-established. Season 5 starts in April you have time to catch up what are you doing go listen to it.
The Foreign Beggars / Dirt Boy Blues - DCC (and then Cyber Sprawl Classics) AP. Two players, good chemistry, good effects and editing.
Romance of the 3 Kingdoms - An approachable abridged retelling of the Romance of the 3 Kingdoms. Rot3k is still super-complex, but the main site has a load of supplementary material to go along with it.
Ologies - Obscure (and sometimes not too obscure) fields of study, straight from the people doing the studying. Great if you want to learn a whole lot about this one very specific field you never considered anyone making a profession out of.
Revisionist History - Take something normally overlooked: golf clubs and property taxes. Jesuit problem solving. The speed of LSAT testing. Poke it and prod it until it opens up like a puzzle box. Thoughtful, thorough, and insightful.
Heaven's Gate - An empathetic documentary of the cult from beginning to end. Highly recommended.
Bad Books for Bad People - Sometimes it's so bad it's good, sometimes it's so bad it's bad, sometimes it's just grotty and weird and dark and bad in that slang way that means it's good. Your being a bad person is non-negotiable. Embrace that shit.
The FPlus - Terrible things read with enthusiasm.
Castle Superbeast - My listening has peetered out over time (these are very long podcasts with very, very long digressions, and after a while the arguments they can find themselves in get really tiresome), but I still dip in from time to time for video game fun times with a pair of very idiosyncratic fellows.
Not Another D&D Podcast - A fun 5e AP. Silly. Lasted much longer than the other 5e APs I tried listening to, which do not appear here because I have forgotten even their names.
The Green Box Podcast - Some guys from r/NightAtTheOpera talk shop about Delta Green. Mellonbread is abrasive but the others are laid back.
The Dollop - Two comedians discuss stories from American (and sometimes Australian or Icelandic) history. Always absurd, hilarious, often terrible. I had to stop listening a while back, as new episodes were just too depressing to continue with - you could really feel the psychic toll the Trump era has had on the hosts, Dave in particular.
Sequelisers - Fixing the bad sequels to good movies. I have to admit I like the first three seasons with their 2v2 competitive format more than the no-teams fourth season - more variety in prompts, more good jokes and more creative proposals.
Role Playing Public Radio - Longrunning AP podcast. Mostly one shots and occasional campaigns. Their Delta Green and Call of Cthulhu stuff is usually top notch, Eclipse Phase is generally solid. Some are hit or miss, but you'll figure out if it's a bust early on. I super-recommend "The Dreamer Below" and "Somewhere Lane"
The White Vault - Multinational team goes to check in on a research station on Ny-Alesund experiencing technical difficulties. The various threads haven't yet pulled together, and it can sometimes really stretch the found footage aspect of things, but it's overall enjoyable.
The Hyacinth Disaster - An off-the-books asteroid mining mission goes horribly, horribly wrong. Probably my favorite of the sci-fi on this list - it's contained, it's got chutzpah, it is probably the hardest science of the sci-fi lot.
Blogs on Tape - Nick Whelan of Papers and Pencils + guest voices read good OSR blogposts.
Science and Futurism with Isaac Arthur - Actual rocket scientists talks about science and futurism. Has been a massive influence in a lot of my Mothership stuff (all those O'Neill cylinders!)
Tides - Exploring biologist is stranded on a planet with incredible tides and bizarre life. Good stuff.
Mission to Zyxx - Goofy sci-fi improv. Delivers on that premise. Does not add additional premises.
Limetown - Creepy modern horror by way of NPR. The second season isn't as good as the first and I wonder if they got too big for their britches with that TV show, but the first season is sterling stuff.
S-Town - The story of a clock repairman in a shitty little town in the south. I actually thought this was fictional for over half of the runtime - it was so idiosyncratic that it just had to be fiction, or so claimed my mind.
Knifepoint Horror - The one horror anthology that is actually an anthology, as I don't think there's an actual throughline on any of these episodes. This is probably part of why i recall enjoying them, but can't remember the contents.
Sayer - Menacing, smooth-voiced AI runs rampant in a decaying R&D arcology tower on Earth's second moon. i stopped listening because the audio mixing was really weird - this 'cast was very quiet compared to everything else, or was it the other way around? Either way, it is pretty fun.
Apocrypals - So how much do you know about Biblical apocrypha? Not enough. Get you some fire-breathing Mary and Solomon meeting the butt-stuff dragon and Thecla the lightning-mage. Contains all the dunking on Paul you want and need in your life.
Nightmare Magazine Podcast - I am a huge coward so "Dan stopped listening midway through the episode because spooky" is not particularly shocking, but consider the number of horror podcasts on this list that I listen to and am just fine with. This is the good shit.
LeVar Burton Reads - It's Reading Rainbow for adults. As one might expect, Burton pulls from an wonderful and diverse pool of authors and features some great sci-fi and fantasy picks.
The Signal - A good hook (alien transmission that drives people mad! It's leaking!) that goes nowhere fast and devolves into nothing at the end.
99% Invisible - Another oddity podcast. Not as funny as Fish or as charming as Closet, but good stuff all the same.
Gastropod - Food science! Food history! Food fun! Learn what a pawpaw is!
The Allusionist - Words are weird, come on and learn how weird they are.
nosleep - It's stories from r/nosleep. It'll work if you are desperate and need to brute-force pass some time, but every single other horror podcast I list here will be better.
Alzabo Soup - Devoted entirely to the works of Gene Wolfe. Absolutely indispensable as a reading aid if you are tackling the Book of the New Sun.
VAST Horizon - Five hours of a woman sobbing, with intermittent untranslated Chinese. Suffers from flashbacks more interesting than the survival scenario at hand, really handwavy science, and a main character who has the audacity to throw a pity-party despite being a war criminal.
Stay tuned for the inevitable Son of the Son of the Podcast Post, releasing 20XX.