They seem to be like blogs - the more I listen to, the more they multiply!
For inspiration, I listen to The Side Hustle Show, and the Smart Passive Income podcast (I am not an entrepreneur, but I love listening to stories of people who saw an opportunity, then worked their backsides off to make something from it!)
For finance, I listen to The Meaningful Money Podcast, The Money to the Masses Podcast, You Need A Budget (YNAB), Financial Conversation @JourneytoSaving, Minding Your Money Minute, and of course, now the Millennial Money Minutes @millennialmoney.
There is also a podcast thread if you have time for more http://forums.rockstarfinance.com/t/best-money-podcasts/343
Which podcasts do you listen to?