I'm an avid podcast listener, and here are some of my favourites off the top of my head:

Radio Lab (science) -- http://www.radiolab.org/

THE science show to listen to. If you're going to listen to anything from this list, this is the show to listen to. It's very well produced and always interesting. Their most controversial show was Yellow Rain (http://www.radiolab.org/story/239549-yellow-rain/).

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Freakonomics (science/economics) -- http://freakonomics.com/

I often consider this show to be Radio Lab's counterpart. Their headline is "exploring the hidden side of everything". Every single episode is fascinating (here is the show "Cobra Effect" to get you started: http://freakonomics.com/2012/10/11/the-cobra-effect-a-new-fr...). The shows all lean toward a very economist-like way of looking at things, so unless you're in the field, you'll enjoy much of the insights that come about because of this.

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Planet Money (economics) -- http://www.npr.org/blogs/money/

Just a well-produced podcast about money and its long-reaching tendrils. Shows usually focus on interesting stories about money/finance that are in the "background" and go otherwise unnoticed by the population at large.

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TED Radio Hour (everything) -- http://www.npr.org/programs/ted-radio-hour/

Basically a radio version of TED talks. However! It's very well produced and every show is basically made for radio. It's not just TED talks with the video part stripped out.

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This American Life (everything) -- http://www.thisamericanlife.org/

The most downloaded podcast for a reason.

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The Irrelevant Show (comedy) -- http://www.cbc.ca/irrelevantshow/

Fantastic comedy sketch group from Canada. Their most famous cast member is probably Mark Meer (Shepard's voice actor in the Mass Effect games). While some of their sketches can fall flat, more often than not they make me smile. Their humour has a very Canadian slant, so unless you're living in Canada, sketches about, say, Canadian law and politics, might be a little more difficult to decipher. :)

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Wait Wait Don't Tell Me (comedy) -- http://www.npr.org/programs/wait-wait-dont-tell-me/

The only show that actually manages to consistently make me laugh out loud in public. It's a news trivia show with a panel of well-established comedians and writers that participate in the game. Highly recommended.

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Honourable mentions include:

To the Best of Our Knowledge -- http://www.ttbook.org/

Snap Judgement -- http://snapjudgment.org/

Intelligence Squared -- http://www.intelligencesquared.com/

Science Friday -- http://www.sciencefriday.com/

Ask Me Another -- http:/...