Most of these comments here just list the names of the podcasts. Please include a description and your personal comments so that others can consider if they might also be interested.
I will just mention a few:
Hardcore History: The name is pretty good description of what it contains. If 2-4 hour episodes that dig into the why and how of a particular topic in history is not for you, then neither is this podcast.
Dan Carlin focus on ideas and not so much on dates. His pods are infrequent and long.
Martyr Made: Started out with the best, most indepth description of the history of the creation of Israel (from about 1880 to 1949) in the form of over 25 hours of content, some of which is seriously depressing. A good showcase for some of the worst humans can do (on both sides of the conflict). Best enjoyed with a pause button and so not for children.
Joe Rogan: (only added here because others have mentioned it). I subscribe but have only listened to a couple episodes. My main complaint is that they are way too frequent and the title is just whomever he interviews so if the name doesn't ring a bell you will have spend a couple hours figuring out if it is worth listing to.
How it began: Stories of how we got particular techs, from refrigiation to computers. Contains music and background sounds so it fells more like a radio documentary than a podcast. Highly recommended, have listened to several episodes multiple times.
Contex: Same author as how it began, but simpler in production and focuses more on the context of something: like Guns Germs and Steel; the wealth and poverty of nations and so on. The podcast is only a few episodes in.
* Tim Ferris show - kinda like the interviews, and really like the experimental mind-set of Ferris
Less often:
* Magic Readalong - Two guys talking 20 minutes about interesting functional programming and life. These are the conversations I wish I would be having with my friends over beer.
* Intelligence Squared - really good traditional british-style panel debates. Often geopolitical in nature. These are the topics we actually do like to discuss over beer.
Sometimes, mostly game-podcasts:
* The Short Game podcast - finally a podcast aobut short-enough games I actually am able to finish :) This is how I found out about Bithell-games {Subsurface,Quarantine}-Circular
* Dad 'n Sons - i.e. the Superbunnyhop and friends
* Cooptional Podcast - still like them, they seem to be holding the course with Genna Bain taking over after John Bain's death
You probably won't get much from it if you're not a UK resident, but I find him to be a great host, despite his issues with stuttering. I highly recommend the Matt Willis episode.
While not strictly a podcast, I'm a huge fan of Comedians In Cars Getting Coffee. In similar vein, he does a great job of interviewing fellow comedians, and makes episodes with people you might not like very enjoyable.
Radio Drama Revival was recommended here on HN. But I still prefer the old-time corniness of a good X-Minus-One or Suspense episode from the Golden Age ;)
For me, it's while mowing the lawn, gardening, and washing the dishes. I used to on public transport, but that's my Duolingo & music time now.
Sometimes I'll listen to a few minutes of a podcast in the morning while shaving & getting ready - Leo Laporte's "The Tech Guy" podcast is great for this, because each support call is usually just a few minutes long.
I sometimes listen to podcasts while exercising or have a long walk somewhere, but I'm more likely to listen to music for that.
Oh - and some of the podcasts I listen to are about music production / music technology. One of my new favorites is the Sonic Talk podcast (even though their website looks terrible), and Pensado's Place is also good sometimes:
In addition to may that others have mentioned such as JRE, Waking Up, Convos with Tyler, my main go-to is:
The Fifth Column - A weekly libertarian-ish take on the news and media, with lots of hilarity, generally while the hosts finish a bottle of listener-supported bourbon. Kmele Foster runs it along with Matt Welch (Reason) and Michael Moynihan (Vice News).
Interviews on a broad bange of topics
Startups and Tech Finance and Economics General Topics Current Affairs Thinktanks Science Leakey Foundation: Origin Stories Bitcoin/Ethereum Indie