I listen to a lot of podcasts every week. I listen while I am driving, I sometimes listen when I am doing chores. Here are the ones that I currently listen to regularly, in the order in which I usually listen.
The Briefing--Every weekday morning, Albert Mohler, the president of The Southern Baptist Theological Seminary, provides an analysis of the days news and events from a Christian worldview. Dr Mohler is a very insightful, articulate speaker who gives a useful commentary on things going on in the world. The podcast lasts 15 minutes (5 days per week).
Coral Ridge Presbyterian Church--Every week, Coral Ridge posts their weekly teaching. Their senior pastor is Tullian Tchvidjian, who blows the doors open on grace. The teachings will consistently give a much bigger picture of grace. 30-45 minutes once a week.
The White Horse Inn--This is a weekly radio program that typically involves a discussion of issues relevant to a "modern reformation". This program introduced me to the topics of "indicatives before imperatives" and "imputed righteousness", both of which have deeply influenced my thinking. The usual hosts are two Reformed guys (Michael Horton, Kim Riddelberger), a Lutheran (Rod Rosenblatt), and a baptist (Ken Jones). 30 minutes each week.
Stand to Reason--This is a weekly call in program hosted by Greg Koukl, the apologist I have learned the most from. He is an enjoyable, engaging man who promotes a thoughtful discussion of faith and values. 3 hours each week.
Let My People Think--Ravi Zacharias is a deeply engaging, thoughtful evangelist and apologist. He has influenced millions around the globe for Christ. It lasts about 30 minutes.
Lifepoint: Insight for Living Australia puts out a short podcast of a few minutes on an intermittent basis based on sermon highlights from Charles Swindoll. He is easy to listen to and easily connects life with the gospel.
Breakpoint: Breakpoint was started by Chuck Colson as a brief analysis of Christianity and worldview issues. It is currently hosted by Eric Metaxas and John Stonestreet. It usually lasts about 4 minutes every weekday.
Also, for what it is worth, I also use the app called Downcast to manage all of my podcast subscriptions. It works well.