Global News Podcast, The History Hour, In Our Time, The Law Show, all from the BBC, along with a few other series. The Guardian Football Weekly, plus whatever news stuff from there takes my fancy. And then in no particular order the 404 Media Podcast (worthwhile tech news), The Last Podcast on the Left (magic and murderers), the QAA Podcast (it was about insane conspiracy theorists and now it's about the US government) and Angry Planet (military affairs and conflicts from around the world). Sorry that there's a heavy American bias, but there's always, and will forever be, the Adam Buxton podcast.
Some limited series podcasts I've enjoyed over the years have been: Things Fell Apart, The Coming Storm, Mike Duncan's A History of Rome and subsequent Revolutions, Sold a Story: How Teaching Kids to Read Went So Wrong, and The Pornhub Empire from the CBC.
Comedy-adjacent: Three Bean Salad, The Socially Distant Sports Bar, Smith and Sniff, The Gargle, Northern News.
Serious factual stuff, mostly about economics and the wonkish technocratic side of politics: Complex Systems with Patrick McKenzie, Odd Lots, Unhedged, Planet Money, The Briefing Room, Origin Story, Conversations with Tyler, The Truth of The Matter, Inside Briefing with the Institute For Government, Cautionary Tales with Tim Harford.
"Page 94", the Private Eye podcast. I can't imagine that either of you two don't know what "Private Eye" is, so what more can I say?
"The Bugle", a satirical semi-political podacast headed up by Andy Zaltzman as well as a relatively small pool of rotating co-casters. It's been around for a long time, so you've probably already come across it. Highly recommended if not.
"The Gargle" is a spin-off podcast of "The Bugle" headed up by Alice Fraser, which is The Bugle "without the politics". A bit sillier, but well worth it.
"Comedian's Comedian Podcast", by Stuart Goldsmith. Another podcast that's been around for many years featuring interviews with comedians but, unlike similar shows, it's much more about the craft and the person being interviewed and never just a box-tick in a promotional tour. The entire backlog is worth listening to if you're even a teensy bit interested in what makes comedy tick.
"Words Unravelled" explains where English words come from and about language in general.
"Lateral". Tom Scott game show, quite entertaining.
"Dice Funk" is D&D podcast that's been around for about a decade or so. While the underlying systems used are handled accurately, the podcast itself is more about the story telling with dice roles for emphasis and less about going through the mechanics.
"Ctrl, Alt, Access" is a podcast about accessibility in video games and, recently, also board games. It's quite matter-of-fact about what challenges people might face and what can be done to work around those, often with a "rising tide raises all ships" attitude. Highly recommended if you like games, practically required listening if you like making them.
"Poor Hammer" is a 40k podcast mostly about the table top and surrounding issues. I don't play but find it interesting, but if you're looking for a lore heavy thing this isn't it.
I do listen to them. But I feel it's worth mentioning as a mark against them, because it annoys me occasionally, that they are fairly new to the hobby. So if you grew up with 40k occasionally they say something that shows their lack of knowledge of the setting or the game or the complex relationship people have with games workshop before the last 5 years. That doesn't seem like that should be a problem but occasionally they snub their nose at people who remember older stuff, whilst complaining that harlequins isn't an army anymore like that is the worst thing games workshop ever did.
I bully them in the comments every time they say something newchap-y, Warhammer is one place in life where I think gatekeeping and general elitist grognardery is 100% justified and Good Actually. We have to hold up some kind of standards. One of them is a Grey Knights main for fuck's sake. They are the original Matt Ward Mary Sue simp army.
I do really enjoy the podcast though. It's one of the few that isn't overly focussed on competetive playing, which is another thing which is entirely bollocks and can fuck off.
I just listened to the new Dan Carlin Common Sense poor guy is watching it all fall apart before his eyes.
Other than that:
Foreign Affairs Interview - for various insights from the US establishment and beyond including top diplomats and ex-policy officials.
GZero World - again another US foreign affairs show, this one is more a light weekend listen.
Looking Outside - if you want something with more of a futurist or corporate fart-sniffing ideas. Hosted by Jo Lepore who is one of those marketing people.
I also do Rest is Politics and Rest is Money but I'm not sure I can recommend either. I'd probably be happy with Rory Stewart and Peston doing a pod together for dull people.
>>469662 Soundcloud, maybe? Although I just looked there if they had the Private Eye one and I couldn't find it and just wound up listening to some excessively BRILLIANT violent rap music. So if you're looking for something in particular, maybe Soundcloud isn't that good.
Any podcast that's available on Apple Podcasts (i.e. practically all of them except for a handful of Spotify exclusives) is also available on any other podcast app via RSS.
I use Pocket Casts, which I think is the best podcast player available; it used to be a paid service, but now it's completely free. It'll sync all of your subscriptions across the web player and the phone app. There is a "Plus" subscription tier, but you don't need it.