Hardcore History by Dan Carlin - Highly recommend this for anyone with even a passing interest in history.
This American Life - extremely high quality and interesting stories.
Radiolab's More Perfect - I think flobaba recommended it on here a few months back. It's exceptionally good - definitely give it a listen
Friday Night Comedy (BBC Radio 4 Comedy) - News Quiz and the like.
The Infinite Monkey Cage - science based comedy podcast from Radio 4
Money Box - UK centric news about Personal Finance. I only listen to it if the topic interests me but it's by the BBC so it's good quality content.
No Such Thing as a Fish - From the writers behind QI
Freakoconomics Radio - covers similar topics to Freakonomics the book
Econ Talk - actually more interesting that it sounds! Hosted by Russ Roberts who interviews various academics across a range of topics.
Stephen Fry's Great Leap Years – the stories behind inventions hosted by Stephen Fry
Ricky Gervais is Deadly Sirius - comedy podcast hosted by Ricky Gervais + minor celeb guest. It's light hearted enough but don't go expecting it to match the standard of the Karl Pilkington days!
My Dad Wrote a Porno - another comedy podcast. Highly recommend this!
Simon and Mayo Film reviews - does what it says on the tin. I only tend to listen if there's an interesting guest on but it's good quality.