Guiding principle should be it is something you don't expect anyone else reading this will have in their feed. So let's just assume we all know about NPR and the like.
For some of the programmes/podcasts below, I've picked an episode I particularly enjoyed. The sheer volume of radio content the BBC produces means there are many excellent podcasts/programmes that go undiscovered (the BBC's own search engine is terrible).
I subscribe to dozens of other programmes not listed below, but to keep this list short, here is a selection that may (or may not!) appeal:
-- SCIENCE-RELATED PODCASTS
CrowdScience: https://www.bbc.co.uk/programmes/p04d42rc/episodes/downloads
Listeners submit questions that are answered by experts. Recommended example episode: Do animals use medicine? https://www.bbc.co.uk/programmes/w3cszv77
The Life Scientific: https://www.bbc.co.uk/programmes/b015sqc7/episodes/downloads
Interviews with leading scientists (mostly from the UK) - the expertise, passion and knowledge of the scientists is always inspiring to listen. Recommended example episode: Irene Tracey on pain in the brain https://www.bbc.co.uk/programmes/m0003qx1
-- WORLD HISTORY, CULTURE AND IDEAS
The Forum: https://www.bbc.co.uk/programmes/p004kln9/episodes/downloads
An eclectic topic each week with three experts participanting in a lively, informative and stimulating discussion. Recommended example episode: In search of the good life: Epicurus and his philosophy https://www.bbc.co.uk/programmes/w3cszjv4
-- DRAMA
The Lovecraft Investigations: https://www.bbc.co.uk/programmes/p06spb8w/episodes/downloads
Inspired by H.P. Lovecraft, this mystery-horror drama features witchcraft, the occult and secret government operations. I found it pretty gripping. All episodes available.
Children of the Stones: https://www.bbc.co.uk/programmes/p08sy3qx/episodes/downloads
Another enjoyable horror-mystery. All episodes available.