Podcasts I listen to for Psychology, the Brain, or related topics:
Hidden Brain - NPR's social science correspondent picks his favorite research topics from behavioral science and discusses them in a fun, news-y, short format!
Invisibilia - Podcast about "the invisible forces that guide our behavior." In-depth, story-driven reporting.
Planet Money - Economics, behavior
Science VS - Gimlet Media's science journalism is entertaining, critical, hilarious, and includes some of the best science reporting out there. Many episodes tackle behavioral science but I recommend the whole show.
Very Bad Wizards - A philosopher and a psychologist discuss issues in morality and ethics. (NSFW warning: Strong language. Middle school humor.)
Episodes I recommend on specific topics:
Planet Money 677, The Experiment Experiment: The Replication Crisis in Psychology. They interview Brian Nosek!