Here are some of my favorite podcasts (and specific episodes).
Freakonomics: What Can Uber Teach Us About the Gender Pay Gap? - A great follow-up to their first gender pay gap episode. Lots of data from a giant Uber study, and some interesting results.
Freakonomics: The true story of the gender pay gap - This one's pretty good.
Science Vs: Attachment parenting - A little outside my wheelhouse, but I thought this was a super-interesting episode. I go back and forth on how much I like Science Vs, but these two episodes were also pretty interesting: Organic Food and GMO...OMG?
99% Invisible: The Sizzle - The weird world of trademarked sounds.
This American Life: Cars - A fun look at the inner workings of a car dealership. Quotas, sales techniques, and what it's like to sell cars for a living. (There's some cursing in this one because, you know, they're in a car dealership.)
EconTalk: Thomas Leonard on Race, Eugenics, and Illiberal Reformers - This one is a little darker, but has some super interesting discussion on the history of some currently-popular political and social causes.
Mystery Show: #3 - Belt Buckle - I think this is my favorite podcast episode. It starts a little slow, but it gets better and better as you listen.
EconTalk: Mike Munger on Price Gouging - A strong left turn into Economics Land™, where they explore why price gouging might be unfairly maligned.
Revisionist History - The Big Man Can't Shoot - Really interesting look at how sports and psychology intersect (plus an indirect Gator Basketball tie-in).
Freakonomics - The Upside of Quitting - It's hard to pick just one Freakonomics episode, but this is a good one.
This American Life - One Last Thing Before I Go - Act 1 (about the phone booth) is really, really good. NOTE: Not in iTunes, but that link should drop you to the page for this episode.
99% Invisible - Structural Integrity - Stories about how architecture reflects the local environment.
Radiolab - Colors - How do we know the sky is blue?