I'm a big fan of spoken word Podcasts, for learning and for comedy, and the following are my personal favourites.

I use Pocket Casts for playback, running at 1.1x speed and with silence removed.

STEM

PC Pro – every 2 weeks, this is a live recording of IT news being discussed along with the "hot hardware of the week". You can listen live, and contribute, via Mixlr, and I'm a regularly commenter.

More or Less – quite possibly my favourite podcast, this deals with the statistics in the news and in life, questioning whether they're correct.

50 Things That Made The Modern Economy – each is a short story about a person or product. Narrated by Tim Hartford, who's behind the More or Less Podcast and is a great story-teller, each one is fascinating and well worth learning about.

The Infinite Monkey Cage – a great science programme, but a little "high brow" for me at times, with many discussions going way over my head. A mixed panel each week of scientists and comedians makes it very lively and interesting.

Language

The Allusionist – a podcast about language. 

Biographical

Desert Island Discs – different people are interviewed about their life whilst choosing their favourite music. I don't listen to all but pick and choose those that I'm most interested in.

Comedy

No Such Thing as a Fish – from the "Elves" that write all the fact for the QI TV programme, this is a weekly, comedic dose of facts and trivia.

Friday Night Comedy – from BBC Radio 4, this is their Friday 6:30pm comedy, usually The News Quiz, Dead Ringers or The Now Show, all of which are excellent satire.

Comedy of the Week – again from BBC Radio 4, this is an assortment of different comedy shows that the station are trying to promote. There are some real gems to be found here.

David Baddiel Tries to Understand – short, comic, but informative investigations into everyday items, from electricity to Kim Kardashian.

WordPress

WordPress Weekly – from WP Tavern, this weekly podcasts gives you all the latest new from the world of WordPress.

Post Status Draft – Quite ad-hoc releases but are often on important subjects or interviews with equally important people.