I listen to a lot of podcasts, especially now that I have a daily 75 minute bicycle commute. Here's a list of my favorites:
Radiolab - It's science-focused storytelling that is absolutely fascinating and incredibly well done meaning that if you're an even mildly curious human being you'll find it utterly addicting.
The Bible Project - The Bible Project is quickly becoming popular for their absolutely amazing videos on each book of the Bible as well as various themes. Producers/masterminds Tim Mackie and Jonathan Collins also produce occasional "companion podcasts" that offer "biblical scholarship in conversation" at a level that is both digestible and fascinating for those who wouldn't typically listen to biblical scholarship podcasts. Amazing.
The Liturgists - Created by two very different Christian dudes both named Mike who both fell away from their Calvinist/evangelical faith and eventually found their way "back" to a very different kind of Christianity. This show will ruffle the feathers of those who feel stubborn in their Christian viewpoints and will bring fresh air to those who have experienced discontent, or even despair toward the version of Christianity you've grown up on.
On Being w/ Krista Tippett - Poets, priests, authors, activists, musicians, scientists, this show draws them all and draws the best out of all of them. She's the best interviewer I know of and she's interviewed the likes of Desmond Tutu, Marilynne Robinson, Jean Vanier, Thomas Martin, and more. If only the whole world would listen to this show...
Seminary Dropout - Host Shane Blackshear has made a successful go at interviewing biblical scholars for others like him who love the Bible and love learning but don't need all the hustle and hassle of seminary. He's a smart, humble host who pulls great guests like N.T. Wright and isn't afraid to be a bit provocative.
The Phil Vischer Podcast - It's the light, funny, sarcastic version of some of these other shows devoted to rethinking their grandpa's Christianity. They get top-notch guests like John Walton and sing funny Ukulele outros. What else would you expect from a show hosted by the creator of Veggie Tales?
The Naked Bible Podcast - Bible scholarship by Dr. Mike Heiser. Some is topical, some walk through books of the Bible, some focus on hermeneutical approaches. Some is fascinating, some feels like a boring grad school class. But all of it is top-notch biblical scholarship right in your earbuds for free.
One of the easiest and most efficient ways to learn new things is to hear authors discuss the highlights of their latest books. Both of these podcasts help you do just that by interviewing a biblical scholar about his/her most recent publication: OnScript and the aptly named New Books in Biblical Studies.