I like listening to historical podcasts, and my favorites are "The History of Rome" (which has finished) and its followup "The History of Byzantium" and "Hardcore History" . I've heard good things about "Revolutions" by the creator of "The History of Rome" but I haven't checked it out yet.
Also I've been enjoying "Fall of Civilizations" a lot, but so far have only listened to a few of the episodes.
I've listened to all of these podcasts besides Hardcore history, and I can highly recommend all of them. It's hard to pick a favourite but it might be Revolutions, which I found the most eye-opening, especially season 3 on the french revolution. I'm currently working my way through Wittenberg to Westphalia, the Wars of the Reformation, which is meant to be on the 30 years way, but takes a very deep dive into the life, economy, history and culture of the middle ages and early modern period.
Anything from Aaron Mahnke (or his company Grim & Mild). I especially enjoy Lore and Cabinet of Curiosities. For true crime, I like Murder, Mysteries and Makeup or The Casual Criminalist.
Hardcore History. The come out a few times a year and are incredibly long (some episodes are five hours), but listening to Dan Carlin talk is really engaging. Plus he has one of those voices you can fall asleep to.
It Could Happen Here. Keeps my righteous anger at ‘the man’ topped up.
Criminal Records. Fun crime podcast focussed on the weird and less heard of crimes in history.
Except this one: The Curious Cases of Rutherford & Fry - Investigating everyday mysteries with lots of science and just as much humour. A well-produced series that has been running for years! The presenters are established scientists themselves.
Behind the Bastards, a deep dive into the various shit people of history. Episode one is Saddam Hussein: Erotic Novelist.
There's nearly 700 episodes, and I've yet to run tio a dud. Loads of great guests. My only gripe is that it's a touch Amerocentric, but other than that I'd recommend it to basically anyone. Not kid friendly, in case that wasn't obvious.
My Brother, My Brother And Me - 3 brothers giving not-so-serious advice to listeners, reacting to questions from Yahoo Answers (when that was a thing), and overall being funny/silly
My Dad Wrote A Porno - 3 people hilariously reacting to an "erotica" book series that one of the guys' dad published (I would say the books are maybe only 5%-20% explicit, depending on the chapter)
No Such Thing As A Fish - the behind-the-scenes staff of the show QI bring up interesting facts and tidbits from history/nature/etc. (each episode is split into 4 parts where each member brings up a fact and the others react to it and bring up related facts)
If I Were You - Jake & Amir from CollegeHumor giving advice to listeners (mostly in a sarcastic/tongue-in-cheek way but sometimes genuinely), mostly about relationships/dating
SmartLess - Jason Bateman and Will Arnett (Arrested Development) and Sean Hayes (Will & Grace) interview a famous person each episode where only one of the hosts known who it is beforehand (it gets better after the first few episodes)
Office Ladies - Jenna and Angela from The Office (US) reacting to each episode of the show and bringing up behind-the-scenes stuff (some of episodes include interviews with other cast members/staff)
I am surprised some of the big ones haven’t been mentioned yet -
Radiolab - Not really sure how to describe this podcast. It’s superb journalism at its core. They do both short and multi-episode long form about a variety of topics from science to history to current events. For example, how dinosaurs died when the asteroid hit earth, the story of a Guantanamo convict with the same name as the host, and how poorly computer databases are designed for names that are outside the norm.
Planet Money - An excellent economics podcast where complex topics are distilled in fairly short episodes. They recently released a completely AI generated episode which was incredibly scary with how good it was.
Serial - One multi-episode series at a time about complicated criminal cases.
What Roman Mars can Learn about Con Law - Started off during the Trump Presidency when tough questions about the US constitution are being asked given his penchant for pushing the legal boundaries and norms.
Paul interviews a different person each week and discuss their journeys on dealing with their mental health. Paul is also been very open about his struggles. It helps that he is a comedian and has a subtle but dark humor that I enjoy.
I also really like the short surveys that he reads and people have filled out on his website because they make me feel connected that I’m not alone.
Throughline has been my favorite since it launched a few years ago. The hosts take a deep dive into the historical events leading up to topical events of the present weaving a thread through them, hence the name.
Some of the examples are the history of policing in the US and how capitalism became the dominant economic system.
Obviously it depends on what you're into but I love tech and gaming. I listen to the wan show, friends per second, trash taste and the waveform podcasts.
Hello Internet - I love the hosts, though the show is over (or, on hiatus if you truly believe)
Cortex- I listen to this mostly because CGP Grey is on it (who also was one of the hosts on Hello Internet). It's also nice for tech news/ productivity information, though sometimes I get a bit frustrated at the show
Dear Hank and John (or Dear John and Hank) - John and Hank Green answer listener questions. I'm really a sucker for this "two guys talk at the mic" format lmao
Dungeons and Daddies- a DnD podcast with Freddie Wong that I find immensely entertaining
Well There's Your Problem - an engineering disasters podcast. I really enjoy listening to the hosts, though they do tend to ramble. I like it, but might not be for everyone
Edit: Almost forgot, Wizards of Waverly Place Podcast. David Deloise and Jen Stone (The dad and Harper from the show) watch old Wizards of Waverly Place episodes and talks about them as well as has guests from the show on. This one can get a bit frustrating for me as the podcast feels a bit rushed, and their social media presence is very click baity. But I find it interesting none the less
I dig My Brother, My Brother, and Me from time to time. It's just three nerdy brothers dorking out together. They used to answer Yahoo questions but they moved to wiki how's since Yahoo died. They good for a laugh but even I admit they can be a handful sometimes lol