Dang, really enjoying reading all these great recommendations; my podcast load is going to be growing (again)!

My personal faves out of my 100+ subs are below. All should be available through a typical podcatcher app. Tried to mark some as NSFW but probably missed some. Some of these are extremely well-known but the question didn't specify "hidden gems".

Part-Time Genius - General interesting stuff

James O'Brien's Mystery Hour - BBC radio program. People call in with questions and answers to (generally) interesting questions.

Stuff You Should Know - Interesting general topics

Irish and Celtic Music Podcast - Best celtic music podcast around IMO

Behind the Bastards - Profiles of evil or otherwise undesirable people/entities in history (NSFW)

Crazy Genius - Interesting topics, sponsored by The Atlantic

In Our Time - BBC 4 science show (very high quality IMO)

Business Wars - Multi-part series regarding company vs. company stories (Blockbuster vs. Netflix and Nintendo vs. Sega are my faves)

Something You Should Know - General info, tends toward self-help and lifehacks

Curiosity Podcast - Curiosity is one of my favorite apps (interesting topics every day) and these are short episodes

Freakonomics Radio - From the same author of Freakonomics

The Changelog - Tech stuff; recent episodes include "Segment’s transition back to a monorepo" and "Istio service mesh and microservices"

Ear Hustle - Interviews with death row inmates; oddly fascinating (NSFW)

Linux Unplugged - Linux stuff

Lexicon Valley - Interesting stories about language

We Hate Movies - Riffing on bad movies; I especially like it when they blast movies I actually like (NSFW)

Skeptoid - Stories for skeptics (of general antiscience etc)

More or Less: Behind the Statistics - BBC4 radio podcast, insight behind hard data

Linux Action Show - Linux stuff

Internet History Podcast - Really more of a 'tech history' podcast; recent eps include "History of Google", "The Epic Fall of Digg", and interviews with folks like CmdrTaco (Slashdot)

Oh No Ross and Carrie - One of my absolute favorites. They investigate pseudoscience and other stuff from the inside out. My absolute favorite series by them is their 9-parter on Scientology. If you're a Scientologist, ignore this recommendation.

Skeptic's Guide to the Universe - Pushing back on the pseudoscience

This Week in Enterprise Tech - Tech podcast; recent eps include "Bullying Black Hat" and "Unikernels and the Death of the Security Patch"

StarTalk - Neil Degrasse Tyson (usually) and occasionally Bill Nye

Mysterious Universe - OK, I generally consider myself mostly rational but can't deny I enjoy listening to "out there" stuff. This is one of the "out there" podcasts with two Australians

How Did This Get Made? - Funny podcast about bad movies (NSFW)

Thirty Twenty Ten - These guys provide a "this day in history" from 30/20/10 years ago. Typically covers pop culture, video games, etc.

Science Vs. - Another very well done science podcast
FLOSS Weekly - Free and open source topics

DogCast Radio - Dog stuff

The Curious Case of Rutherford and Fry - ANOTHER well-done science podcast from BBC Radio

Foot Stompin Free Scottish Music - Free Scottish music. If it's not Scottish, it's crap!

Late Night Last Week - Condenses all of the late night comedians. Host is kind of preachy and annoying, come for the content though (NSFW)

Dan Carlin's Hardcore History - Best history podcast on the planet

Seincast - Going through every Seinfeld episode; they've concluded their run now. Breaks down the minutia and trivia from each episode, each scene.

The Weirdest Thing I learned this Week

Disgraceland - Pods about wild musicians

Hello From The Magic Tavern - Guy falls through a
dimensional portal in a Burger King to the magical land of Foon. Radio-play style, I find this hilarious and well done.

Artificial Intelligence - Recent interviews with Christof Koch, Ray Kurzeil

Eddie Trunk Podcast - Interviews rock/metal musicians

Awkward Human Survival Guide - NSFW, adult topics

NPR Shows, BBC Shows