There are a number of podcasts targeted at authors. Here are my favorites:

The Creative Penn hosted by Joanna Penn. This is my all-time favorite writing related podcast. Joanna is a savvy and enthusiastic author entrepreneur who provides fantastic business and marketing information. Her optimism is my antidote to the negativity often expressed in the industry. Plus, I love the way she explores new niches and trends in publishing.

How Do You Write hosted by Rachael Herron. Fascinating interviews where authors reveal details about their writing processes.

The Petal to the Metal with Rachael Herron and J. Thorn. Down-to-earth conversations about what it's like to be a full-time writer.

The Smarty Pants Book Marketing Podcast hosted by Chris and Becca Syme. Actionable marketing advice for fiction and non-fiction writers.

The Self-Publishing Podcast with Johnny B. Truant, Sean Platt, and David Wright. The language is definitely not suitable for work, and they often go off-topic, but these guys are dedicated to making their author careers stick and aren't afraid to experiment. Their stories of what's working and not working for their business, and their future plans for optimizing their business, are bound to give indie authors some good ideas. Worth listening to even if just for the banter.

Mark Dawson's Self Publishing Formula hosted by Mark Dawson and James Blatch. They discuss self-publishing with a variety of people in the industry.

The Rocking Self-Publishing Podcast hosted by Simon Whistler. NOTE: Simon has retired this podcast. However, as of January 2018 you can still use the URL to access old episodes. Interviews with the top authors in the self-publishing industry. Focuses mostly on the stories of how the authors rose to success. Valuable for those looking for inspiration from others who have achieved their goals.