I've added a few of these to my feed to test out. I'm always looking for new options. Here's a selection from my ever-growing queue. As a note, I typically like shorter podcasts (less than 1 hour) and don't find podcasts with celebrity guests that interesting.
Currently Running -
Reply All - Probably my favorite that's still running. Wide variety of stories loosely tied to the internet/technology. They do some really good stories.
This American Life - The OG podcast about a wide range of personal stories and experiences.
Criminal - Unique stories about crimes and criminals. Not your typical crime podcast.
Invisibilia - About the "Invisible Forces that affect our lives." Mainly a range of personal stories about people that differ from me. I'm always impressed with the range of stories they find and how they can tie them together.
Heavyweight - The host is a great story-teller. He tells stories of every day people, but in a funny & self-depricating way.
Ear Hustle - A podcast from inside the walls of prison.
The Allusionist - This one is pretty niche, but I love it. It's an amusing podcast about etymology.
Embedded - A series of investigative reports from where the news is happening. Season 1 is especially great (Season 3 is not).
In The Dark - Captivating serial podcast about crimes & investigations and what they got wrong.
30 for 30 Podcast - Well produced audio docs, like the 30 for 30 TV series.
The Dollop - Two comedians laugh their way through weird stories from history.
How I Built This - Entrepreneurs tell their stories about the companies they built.
Freakanomics Radio - Sociology meets Economics.
Others: Stuff You Missed in History Class, 99% Invisible, Lore, Science Vs, Endless Thread, Stuff You Should Know, Small Town Murder, The Pitch, Answer Me This, No Such Thing as a Fish, Crimetown
Previous Series/Podcasts:
S-Town - A captivating serialized podcast about a character in a small town that grows in intrigue with each listen.
Mystery Show - Similar to Heavyweight, but just so, so good. One of the best written podcasts ever.
Serial - Even though I think Season 4 isn't ruled out, I include this here because Season 1 is just stand-alone remarkable. It changed the game.
How to Do Everything - A long-running podcast from 2 great hosts that talk about what's going on behind every-day things. They were great.
Homecoming - Fictional miniseries by Gimlet that was made into an Amazon series.
Caliphate - A series from one of my favorite reporters: Rukmini Callimachi. She was on the ground covering ISIS and knows more about the organization than just about anyone else. Super interesting.
The Drop Out - A series that covered Elizabeth Holmes and Theranos, basically a female version of the Fyre Fest dude.
Sandra - Another well-produced fictional miniseries from Gimlet.
We have a lot of overlap. Popculture & sawbones are the only two I've not heard. I'll check them out. Any specific episodes you'd recommend on those two?
Full disclosure, I happen to know one of the hosts of Pop Culture Therapists. The episodes over Silver linings Playbook and 13 Reasons Why are good starters though. I don't know if it's for everyone because they often joke about serious topics kinda like how doctors or cops do. A bit of dark humor.
The sawbones episodes on Lobotomy, Mercury, and typhoid Mary are interesting if not a little gory. In fact they don't beat around the bush and sometimes the descriptions are a little graphic/gruesome but still very interesting. It amazes me what we used to do in the name of medicine and health.
The Dollop sounds great and I'll be adding that to my rotation.
The Indicator Planet Money Crimetown Meateater The Wild JRE, sometimes Hardcore History (Blueprint for Armageddon series is the best set of podcasts ever made, IMO) How I Built This has some good ones Ben Shapiro if some juicy political news comes out Stuff You Should Know, sometimes TexAgs Radio, in the fall after football games Industry Focus, if you're into finance Pardon My Take (Barstool Sports podcast)
I listen to Lore and Conan Needs a Friend (which have been mentioned), so I'll throw out another one I love: Cocaine and Rhinestones. It's put on by David Allan Coe's son, and he focuses on stories surrounding country music in the 1900s. Some of the topics include Okie from Muskogee, Harper Valley PTA, The Pill, Spade Cooley killing his wife, and a bunch of others.
Figured I'd update this thread with a few newer ones I'm listening/have listened to.
Wind of Change - Did the CIA write a hit song? The Left Right Game - Probably the best fiction podcast I've listened to Your Own Backyard - Investigating the Kristen Smart Disappearance Conviction, Season 2: American Panic - About the Satanic Panic. It's nuts. Every Little Thing - I'd listened to this one in the past, but have been catching up on them more now. Bite sized episodes about random questions we have. Man in the Window - Investigation of the evolution of the Golden State Killer Slow Burn, Season 3 - The story of Tupac vs. Biggie The Clearing - A woman investigates whether her father was a serial killer.