Updated 10 Dec 12, please use comments to send me news of new podcasts or dead links etc.
Group Therapy on London's Resonance FM - Each week, a 'confession' is posed to a panel of three commentators (a psychologist, academic and comedian) who come together to explain the universal themes and theories around the problem, offering insights and opinions along the way.
The Psychology Faculty
Psychology of attractiveness podcast
Royal College of Psychiatrists
The American Journal of Psychiatry
My Three Shrinks
Shrink Rap Radio
All in the Mind (ABC Radio)
Neuropod (from the journal Nature in association with the Dana Foundation)
University of Nebraska
The Dana Foundation
The Institute of Psychiatry
The University of California Berkeley - 1, 2, 3
University of Connecticut
The National Institutes of Health
This Week in the History of Psychology
Coach radio (work psychology)
Brain science podcast with Dr Ginger Campbell
General science podcasts (they often feature psychology) :
The New York Academy of Sciences
Science Times (link opens in iTunes), from the New York Times
If you know of a psychology-related podcast that I've omitted, please let me know via comments and I'll add it to the main list.
This list wouldn't have been possible without Mind Hacks' Vaughan Bell.