Repeating what many have mentioned...
Radiolab is my all time favorite. I try to explain it to people "they pick one topic, like sleep or love and come at it from interesting angles, then they interview experts and do trippy things with the sound editing..." Yeah, I'm probably not upping their listening base with that endorsement.
This American Life is my second favorite. I tried to submit a story idea to them, but alack alas, they did not contact me :(
I loved Serial, but I'm not as excited for the second season. I feel like Making a Murderer was the second season of Serial ...
I like The Moth, but it's hit or miss.
And I tried listening to Radical Personal Finance, I really did (isn't the host on here? sorry man...) but it was just too rambling, not enough guests to mix it up.
I always get disappointed when I download a bunch of episodes of a new (to me) podcast for a road trip and then I don't like them. We listened to Welcome to Nightvale in the creepy areas of New Mexico and Arizona (you know where I'm talkin bout) but I kept wanting it to have an overarching story line, and it didn't. I like the concept though.
I like Wait Wait Don't Tell Me and Car Talk, but I hardly think of them as podcasts since I usually catch them live. (aww, except its all reruns of cartalk now... rip) I really wish my local public radio station had more programming and less classical. Saturday and Sunday mornings and afternoons had the best programming with my home stations in IL and CT.
I'm mostly rambling on here so I can follow this thread and keep getting suggestions for new ones.