As a very big fan of audiobooks, I was probably always likely to love podcasts too. When I tried them I found that I really did and have become pretty hooked. I find them easy to dip into and because I subscribe to quite a few I can often find a 5 minute listen for when I'm making a cup of tea or a 60 minute listen for when I want a nice long soak or walk. Here's a round up of some of my favourites (in no particular order), although I listen to many others and hope my list will keep expanding!
10 Fascinating Podcasts: Part One (1-5)
Psychology in Everyday Life: The Psych Files
Try this episode: The Psych Files is a podcast for anyone interested in the topic of psychology and how ideas in this field apply to everyday life. Dr. Michael Britt brings you an upbeat, fun podcast of interest to everyone from psychology majors to those just interested in why people do what they do. 
Explorations in the world of science. A podcast from the BBC World Service. Try this episode: Discovery
Point of Inquiry is the Center for Inquiry's flagship podcast, where the brightest minds of our time sound off on all the things you're not supposed to talk about at the dinner table: science, religion, and politics. Guests have included Brian Greene, Susan Jacoby, Richard Dawkins, Ann Druyan, Neil deGrasse Tyson, Eugenie Scott, Adam Savage, Bill Nye, and Francis Collins. Point of Inquiry is produced at the Center for Inquiry in Amherst, N.Y. Try this episode: Point of Inquiry
Melvyn Bragg and guests discuss the history of ideas. Try this episode: In Our Time
A two-time Peabody Award-winner, Radiolab is an investigation told through sounds and stories, and centered around one big idea. In the Radiolab world, information sounds like music and science and culture collide. Hosted by Jad Abumrad and Robert Krulwich, the show is designed for listeners who demand skepticism, but appreciate wonder. WNYC Studios is the producer of other leading podcasts including Freakonomics Radio, Death, Sex & Money, On the Media and many more. Try this episode: Part two coming soon... Do you listen to podcasts or do you have your own podcast? I'm always keen to hear recommendations! 
