These are my favorites.

Daniel and Jorge Explain the Universe

• A fun-filled discussion of the big, mind-blowing, unanswered questions about the Universe. In each episode, Daniel Whiteson (a Physicist who works at CERN) and Jorge Cham (a popular online cartoonist) discuss some of the simple but profound questions that people have been wondering about for thousands of years, explaining the science in a fun, shorts-wearing and jargon-free way.

StarTalk Radio

• Science, pop culture, and comedy collide on StarTalk Radio! Neil deGrasse Tyson, astrophysicist and Director of New York's Hayden Planetarium, and his comic co-hosts, guest celebrities, and scientific experts explore astronomy, physics, and everything else there is to know about life in the universe. New episodes premiere Tuesdays. Keep Looking Up!

Unexplainable

• Unexplainable takes listeners right up to the edge of what we know ... and then keeps right on going. This Vox podcast explores scientific mysteries, unanswered questions, and all the things we learn by diving into the unknown. New episodes every Wednesday.

Fall of Civilizations Podcast

• A history podcast looking at the collapse of a different civilization each episode. What did they have in common? Why did they fall? And what did it feel like to watch it happen?

Literature and History

• With millions of downloads, hundreds of hours of soundtracked content, and an overall emphasis on the cultural history behind famous works of literature, Literature and History is one of the most popular independent podcasts on its subject. Starting with Sumerian cuneiform in 3,100 BCE, Literature and History moves forward in chronological order through Assyriology, Egyptology, the Old Testament, Ancient Greece and Rome, and the birth of Christianity. The show's current season is on Late Antiquity (or 200-700 CE) and the dawn of the Middle Ages. A typical episode (they average about two hours) features a general introduction to a work of literature, then a full summary of that work that expects no prior knowledge, and finally, an analysis of the cultural, biographical, and historical forces that gave rise to the work in question. Original symphonic and ambient background music is woven throughout each show, and all episodes offer free full, illustrated, footnoted transcriptions as well as quizzes for purposes of review. The show has no advertisements, and its host takes pride in a professional approach that avoids chitchat and ephemera and gets straight to the educational content. You can listen to the episodes in any order, although most listeners begin at the beginning and proceed from there, as the podcast itself is chronologically organized. Doug Metzger finished his Ph.D. in literature in 2011. His chief scholarly interest, following his dissertation work, continues to be 19th-century realism and postbellum American philosophy.