Seriously, no mention of Radiolab yet? Great podcast, they are brilliant at creating audio. Their work almost creating a new medium. The most memorable to me at this moment (without actually checking the archives) is the one about Henrietta Lacks.
You got News Quiz already, that's the one that makes me laugh the most. The US Wait Wait Don't Tell Me is not as smart, but ok.
I find the Oxford Dictionary Biographies strangely fascinating. They are very much cold readings of biographies of people I have never heard of, but they are fascinating, like the person who create the occupation "Tattoo Artist". Tolkien is waiting in my queue -whom I have obviously heard of - be interesting if it's still as good with knowledge. I've just discovered they have done 250 podcasts, so I could spend the rest of my life catching up.
In Our Time is good, too, but requires focus.
Savage Love is good, if you can listen to a thoroughly out gay American give sex advice. Don't listen it it, if that doesn't appeal. Dan Savage recently published a letter I sent him (not on the podcast) and I am so proud, but can't share it with anyone as it tells too much about me.
This American Life. OMG, just brilliant. That's how I discovered The Moth (mentioned above)
also, +1 to most of the posting above.