In order of my podcast app (which is iCatcher! by the way):

99% Invisible

A Cast of Kings

A Way With Words

Clockwise

Conversation Parade: An Adventure Time Podcast

Criminal

Dan Carlin's Hardcore History

Documentary of the Week (BBC)

Faculty of Horror

Freakonomics Radio

Fresh Air

A Game of Microphones

Game of Thrones the Podcast

Gastropod

Grammar Girl

Here Be Monsters

How Did This Get Made?

I Was There Too

Incomparable (Superfeed)

Inquisitive

Invisibilia

Latest in Paleo

Love + Radio

My Brother, My Brother and Me

Mystery Show

Orange is the New Cast

Planet Money

Pop Culture Happy Hour

Quackcast

Radio Nutrition

Reply All

Roderick on the Line

Savage Lovecast

Sawbones

Serial

Silver Screen Queens

Slate's Culture Gabfest

Slate's Double X

Slate's Spoiler Specials

Slate's The Gist

Start Up Podcast

Studio 360

Sword and Scale

TED Radio Hour

TedTalks

Thank God I'm Atheist

The Broad Experience

The Flop House

The Godless Spellchecker

The Moth

The Nutrition Diva

The Skeptics' Guide to the Universe

The Walking Deadcast

The Weekly Planet

This American Life

Throwing Shade

Useless Information

Watching Dead

WTF

You Are Not So Smart

You Made it Weird

Your Health NPR

Particular Favourites <3

Happy to discuss why the favorites are the favourites if anyone is interested in one!