I listen to a bunch of the stuff already mentioned, and a few things I haven't seen already.
Top 3:
Mom and Dad are Fighting -- Honestly, I don't generally like kids, and I don't intend to have any of my own for a while, but this show is incredibly entertaining in that the hosts are interesting and their attitudes about parenting are refreshingly non-hysterical (though of course sometimes I disagree with them).
Savage Love
-- Podcast about sex & relationships, kinks, and non-vanilla & PC stuff. Dan's views have really changed my perspective on monogamy and opened my mind.
On Point
-- In depth show about various topics where they'll bring in experts and also take calls from viewers. Me loves Tom Ashbrook. Some of the stuff is (I have to say it) so. on. point. (!)
Others:
This American Life
Serial (serial show from This American Life, just started and super interesting)
The Moth
Radiolab
Ask Me Another
Snap Judgement
Pop Culture Happy Hour
Planet Money
Freakonomics
Wait Wait Don't Tell Me