The Daily Show with Trevor Noah: Ears Edition; StarTalk Radio; various NPR podcasts; and my guiltiest pleasure are the older episodes of Hollywood Babble-On and SModcast. Admittedly, Kevin Smith's puerile toilet humor is grating, abrasive, and possesses the subtlety of a wrecking ball, but it got me through some very hard times when I was younger.
Also: Ologies. Simply a mesmerizing show.