Current favorites:
99% invisible
Articles of Interest (on hiatus)
Serial (takes long breaks)
Revisionist History
Cautionary Tales
Behind the Bastards
The Economics of Everyday Things
The Past and the Curious (for the kids)

Podcasts I don’t listen to you much anymore, though they have some good episodes: Deep Cover
Radiolab
This American Life
The Moth
Odd Lots
Animal Spirits Podcast
Dan Carlin’s Hardcore History