Philosophy Bites is perhaps the granddaddy of philosophical podcasting. David Edmonds and Nigel Warburton interview philosophers graciously and insightfully. When I was starting out this was my go-to. Each podcast lasts no more than twenty minutes and yet manages to cover a topic succinctly and sufficiently.
In Our Time is hosted by the inimitable Melvin Bragg who readily admits his limited background in philosophy. This is a distinct advantage as he will interject at the slightest whiff of an interviewee careering off into some highly technical phi-jargon. The discussions are usually between Bragg and three experts in the field and are fairly sweeping in scope covering movements, figures and historical eras in philosophy.
Elucidations is the product of the University of Chicago. Philosophers are interviewed about a range of topics and offer some insight into contemporary debates. The discussions are similar to Philosophy Bites but longer, deeper, and often more specific.
Patterson in Pursuit. I am a big fan of this podcast. Patterson excels at taking you on his journey of discovery. He has a rather intriguing anti-establishment bent and this means he is not shy of disputing some of his interviewees. Indeed, some of his interviews are edited to include his running commentary. I enjoyed his debate with a professor from Columbia University about whether or not contradictions are possible. Where some might fawn, Patterson pursues.
New Books in Philosophy is a series of interviews with philosophers about their new books. The interviewers are philosophers and so offer good summaries of their interviewees’ books. The discussions can be a little dry but if you are looking for a way to keep up with the latest book releases in a wide variety of topics in philosophy, then this one’s for you.