So I'm not sure if I'm slightly off topic but I listen to YouTube mostly rather than podcasts however a number of the channels I frequent also do podcasts.
The Thinking Atheist
Godless Engineer (funny AF, thoughtful)
Godless Cranium (Canadian thoughtful and informative)
Holy Koolaid
The Nonsequitor Show (hosts debates about many topics)
The Geek Room (usually hosts Nonsequitor after shows)
Vices Rhino (Canadian funny and informative)
Genetically Modified Skeptic (thoughtful and informative)
Prophet of Zod
AronRa
Hiith
Logicked (Canadian)
Armoured Skeptic (Canadian)
Chris Shelton (ex-scientologist)
Cult of Dusty
MrCreepyPasta a lot of creepypasta channels.
Sigh I'm just going to end the list there.

The Partially Examined Life. It's all about philosophy. It's 3 people discussing different aspects of different philosphers across history. They have links you can go to find the original works and read up before the discussion if you want.

I'm really glad you started this thread. I've been having a lot of fun finding new podcasts because of this.

takes a deep breath MBMBAM, the adventure zone, critical hit, drunks and dragons, nerd poker, sawbones, fictional, lore, myths and legends, welcome to nightvale, small town murder, comedy bang bang!, jordan, Jesse go!, judge John hodgeman, we hate movies, all of star talk, waking up with Sam Harris, IQ2, radio lab, song exploder, bunker buddies, how cast, pod castle, pseudopod, escape pod, the HP Lovecraft literary podcast, game of microphones, a cast of thrones, the game of thrones podcast... I'm sure I'm missing a few. I listen to a lot of pod casts apparently, lol. Surprisingly I'm up to date on all of them too. 0.o

The Thinking Atheist; Cognitive Dissonance ; Atheist in the Trailer Park: Hidden Brain: Stuff to Blow Your Mind; The Way I Heard it (mike Rowe);

I listen to WTF, Fresh Air, This American Life, The Moth, and one or two others.

I spend a lot of time in my car.

One of my ex's? pissed at me?

I watch Dudesoup. It is mainly a video game podcast, but they cover many topics. And they are subtly atheist/agnostic.

Radiolab
The Thinking Atheist
Don't Close Your Eyes (live radio theater)
This American Life
Cognitive Dissonance
Levar Burton Reads
TED Radio Hour
Waiting 4 Wrath
Invisibilia
Do The Right Thing (this one is by far the funniest podcast out there. I wish there were more episodes).
Harry Potter and the Sacred Text

LOVE LOVE LOVE podcasts!

Favorites that I regularly listen to during my 2 - 2 1/2 hours on the road five days a week - and highly recommend.

Code Switch (Race, identity)
Dear Sugars
Death, Sex & Money
Love + Radio
Make Me Smart with Kai Ryssdal and Mollie
The Moth
Planet Money
Relationship Alive (sometimes)
Terrible, Thanks for Asking
This American Life
This is Actually Happening
Wait Wait Don't Tell Me
Waking Up (dupe of yours)

Bill Burr’s Monday Morning Podcast and his Thursday Afternoon Just Before Friday Monday Morning Podcast.