I'm a scientist (and make a science podcast) so I've gone around listening to a lot of science podcasts out there. I figured I occasionally see people interested in podcasts you can learn from, so I figured I'd put my list up here! I've put things into a couple categories -- there is a blurring of the lines here, as some topic-oriented podcasts also interview people in little segments, etc.

Topic-Oriented

Sawbones - A couple that includes an MD discuss different science topics each week, usually medical science and debunking misconceptions.

Science Vs - Very well produced and researched science topics released weekly

Short Wave - Releases every weekday, it is a science podcast from NPR focusing on science news

Patient Zero: Lyme Disease - A public radio miniseries on Lyme disease. Really gets into the details, but is still very accessible!

Weirdest Thing I Learned This Week - The editors of Popular Science magazine collect up weird science-related stories that don't usually end up published but are fun to talk about

Just the Zoo of Us - A couple pick one animal each week to look up facts about and then share them with one another. Great for people that just like to learn about fun animal facts!

Every Little Thing - Listener questions get answered, often with the help of a guest scientist

Interview-Oriented

Ologies - Very fun and illuminating interviews with professionals that study some sort of "-ology", generally science-related.

Carry the One Radio - Science topics and mini-series from UCSF students

Science Friday - Pretty famous radio show/podcast from NPR about science news with interviews involving the scientists that made the discoveries that made the news.

Endocrine Disruptors - Interviews with scientists that study the endocrine system, including endogenous and exogenous chemicals that can influence it