My three favorite podcasts -

Radiolab - nice variety of psych, science, and good story telling. They did an offshoot series called More Perfect that dealt with the Supreme Court. It was really really good. Funny thing about that one - I always thought the theme song for it sounded like something DB would/could have written (I'll see if I can track it down).

The Infinite Monkey Cage - another science-y one.

This American Life - I've been listening to this one long before the concept of podcasts were a thing...back when you had to catch it on the radio. Ira Glass is a super producer of the medium.

And the last one I'd recommend is called The Mystery Show. It's quirky and fun but sadly short lived so you can easily listen to them all. Hoping for a season 2 from this one.