By far and away my favorite is The Chip Race with David Lappin and Dara O'Kearney. Every episode contains interviews with players or industry insiders, hand breakdowns and news.
DAT podcast is also good but dominated now by Negreanu (a good or bad thing deciding on personal preference) along with Adam Schwartz and Terence Chan.
The Grid with Jennifer Shahade is also excellent. She is working through every single hand combination with poker pros. Once the combo is chosen, that's it - the idea to fill in the grid to completion. The pro explains why they played the hand and why it was significant. Conversation naturally then broadens to the players background, poker history etc.
Pokernews is pretty good, and there are many teaching podcasts which are of use but can be a little dry for my taste.