I know it’s a little late in the game, but I have started trying out different podcasts. My favorite right now is Mo Rocca’s “Mobituaries”, in which he discusses people, places and things that are no longer with us… sometimes for the better 
. I have listened to stories about Marlene Detrich, Sammy Davis Jr., Wishbone, and a fascinating piece on names that are no longer popular. Loving this.
What podcasts strike your fancy, and which ones should die an awful death?
I found Rachel Maddow’s first two podcast series, Bag Man (about Spiro Agnew’s fall from grace) and Ultra (about right-wing extremism in the U.S. prior to and during WWII) to be very interesting, and told me about things of which I was unaware.
Both of them are self-contained series (about 6 one-hour episodes each, IIRC), so not a big ongoing commitment, but I know that Maddow is a polarizing figure, so she may or may not be your cup of tea.
A History of Rock and Roll in 500 Songs
The most wonderful podcast in the history of podcasts. Start from the beginning.
Seconding the 500 Songs podcast (and if you can afford it, subscribe to Andrew Hickey’s Patreon for the bonus episodes, many of which are just as good as the regular podcasts).
I’ve also started listening to the country music podcast Cocaine and Rhinestones, which is also really good. And I don’t really even like country music!
Thirding 500 Songs. My contributions:
Slate Political Gabfest (Emily Bazelon and John Dickerson are people whose opinions matter to me. They are very smart and analytical - traits lacking in today’s media landscape)
Penn’s Sunday School (Penn Jillette of Penn & Teller - very interesting guy with some odd opinions, and he’s the first to discourage you listening to him for advice)
Came here to recommend these and I wholeheartedly agree. Fascinating stuff if you are interested in political history. Big thumbs-up.
Behind the Bastards can be interesting (can depend on the person they are discussing). The two-episodes on Clarence Thomas were enlightening and scary (scary a person like him makes it to the Supreme Court). (I linked to Apple for the description but available on most podcast services.)
I REALLY love Dan Carlin’s podcast Hardcore History. Not sure he is still doing them and (I think) you have to pay for them now but well worth the money if you like a deep dive (many hours long) into wars. “Blueprint for Armageddon” was just amazing. Great for those really long drives.
I listen to it every week and have seen them live the few times they have had an event in Chicago (last was a few weeks ago for their anniversary podcast…some of that clapping you hear is me 
).
I like Slate’s Decoder Ring which does a deep dive in to cultural relics, they did one on the mullet that was really interesting. I also liked the first season of My Dad Wrote a Porno.
My favorite Podcast that isn’t about my gaming hobbies is 99% Invisible.
The best podcast I have ever heard is Reply All. It was a product of its moment, though, about tech and web culture, so it might seem a little dated. But man is it cool. Great tech journalism by some wonderful, goofy men.
Right now I’m enjoying Cal Newport’s Deep Living podcast. He’s a very sensible productivity guy, most famous for the book Deep Work, so his podcast is one half productivity advice for knowledge workers and one half tech commentary - most recently he provides a lot of accessible information about AI.
In the history category you can’t beat Dan Carlin’s Hardcore History for super deep dives. I also like The Rest Is History and We Have Ways Of Making You Talk for discussions with a bit of humor thrown in.
I started listening to podcasts about a year ago, and now I listen to them daily on my walks in the mornings, afternoons, and evenings.
For news, I listen to ‘Up First’ and ‘Consider This’ on NPR. For light entertainment, I listen to ‘Heavyweight’. For true crime, I listen to ‘48 Hours’, ‘Dateline’, ‘Hands Tied’, ‘Morbid’, ‘American Criminal’, and ‘48 Hours’. I also listen to ‘Fresh Air’, ‘Hidden Brain’, ‘Throughline’, ‘Cautionary Tales’, ‘Planet Money’, ‘Freakonomics Radio’, and ‘TED Radio Hour’. There are a few others that I occasionally listen to, but are not worth listing.
500 Songs is a given as is the recommendation that the bonus episodes are will worth the modest cost.
I also dig a couple pods that scratch the pop culture nostalgia itch for the 60-something male: The Dana Gould Hour (never just an hour) and Fun for all Ages.
I listen to Science podcasts like Ologies with Alie Ward, A Problem Squared with Matt Parker and Bec Hill, and That’s Absurd Please Elaborate with Trace Dominguez and Julian Huguet. Also comedy chat like Threedom and The Lonely Island and Seth Meyers Podcast.
The Pluribus Podcast, for me is part of the experience of Vince Gilligan’s new show (as well as the Breaking Bad and Better Call Saul Insider podcasts were). The thing that makes them so great is the positive and supportive attitude of everyone involved. It’s so refreshing to listen to a group of folks so enthusiastic and proud of the team they’re working with to create the series. .
Adding another vote to Behind the Bastards and Hardcore History.
My additions: Some More News (if you aren’t 100% sick of the news; former Cracked.com alumns Cody Johnston and Katy Stoll); The Dogg Zzone 9000 (more former Cracked members, Seanbaby and Robert Brockway, discussing cursed media of yesterday and occasionally today).
I don’t think this violates the “concerts” prohibition…
My all-time favorite podcast, which discontinued about three years ago but old episodes are still available, is The Roadhouse by Tony Steidler-Denison. He plays a good cross section of blues artists, with a bit of an emphasis on living, not-so-famous performers who are very good in this commercially iffy musical idiom, or “The Finest Blues You’ve Never Heard!” It’s a great introduction to people who like the music but don’t know a whole lot about it.
I intend to follow through with some of the recommendations provided in this thread. Other than the two I routinely listen to (more on that in a moment), most of the ones I’ve tried have failed to resonate. Supposedly Amy Poehler’s podcast is a laugh a minute; I listened to fifteen minutes of the first episode and couldn’t get into it.
Anyway, the first of the two I listen to is Middling With Eden & Brock, which is an episode-by-episode rewatch podcast of the TV series The Middle. Eden Sher, who played Sue Heck, and Brock Ciarlelli, who played Brad Bottig, go through each episode of The Middle, one by one, starting with 101 and continuing, presumably, until the final episode of the series. Right now they’re on 312, I think. They’ll have guest stars and such, and Q&A’s and all that.
The other is Misfits with Kari Byron and Tori Bellici. It’s about Mythbusters, but rather than review it episode-by-epidsode, they just kind of talk about whatever topic is on their minds that day, and most of the time, it relates to Mythbusters. They, too, will oft have special guests (many of whom have had no connection at all to Mythbusters save for their involvement in something adjacent to the topic of one episode or another), Q&A’s, the whole bit.
Seconding Dan Carlin. I’m anxiously awaiting the next installment of his current Alexander the Great series. But he can be a little intense, especially when he deep dives into historical battle scenes at the personal level.
I’ll add Patrick Wyman’s Tides of History. First, he’s an excellent speaker and storyteller, but his ability to condense volumes of source material (and making it clear where the gaps and controversies are) while still being entertaining is nearly unmatched.
I’m currently working through his series that takes on the progression from deep pre-homo sapient prehistory and am currently in the early Bronze Age. Dunno how far he takes it, I’m still a couple years behind. He does an excellent job making it not just a series on European and near-east stories, but takes the wider view of what was going on all over the world. And every few episodes or so, he interviews a guest scholar with expertise on the subject off whatever the recent episode was.
He has so many episodes that finding a good start point can be daunting, I went back to the 2021-ish episodes where he started this progressive run from pre-history on. I think before that, he did more of a self-contained, scattershot approach.
Oh, man. How’d I forget Behind the Bastards?
Easily one of the best.