Here are some of my favorite podcasts:

Company

Leadership

• Effective Engineering Manager
• The Important Thing with Michael Lopp (aka Rands in Repose)
• Level-up Engineering. A deep look into engineering leadership.
• Manager Tools and Career Tools.
• Soft Skills Engineering. A humorous look at the non-technical skills of software engineers. The hosts always have the great advice of "quit your job".

Business

• Akimbo: A podcast from Seth Godin
• Ditching Hourly with Jonathan Stark
• Rework from Basecamp
• At the Table and The Working Genius Podcast with Patrick Lencioni. Two great podcasts hosted by Patrick Lencioni. One is about business in general, the other about the Working Genius framework to help teams work better together.

Software Development

• Smashing Magazine
• Syntax. Scott Tolinski and Wes Bos cover the latest Javascript and front-end technologies.

Productivity

• The Jordan Harbinger Show
• The Tim Ferriss Show

User Experience

• User Defenders (unfortunately on hiatus). A great podcast on how user experience matters.

Entertainment

• Darknet Diaries.
• Lore and Unobscured are podcasts where the dark and the historical intersect.
• Imaginary Worlds discusses fictional worlds and how we suspend our disbelief.
• The Way I Heard It with Mike Rowe.