My favourite podcasts are:
Cog Dog Radio - Sarah Stremming from The Cognitive Canine blog talks through case studies of her clients as a canine behavioural consultant, and discusses specific behavioural challenges. She presents in a thoughtful manner, is engaging with her audience and is more than happy to revisit and clarify things she has previously said when the correspondence she receives indicates that it was misinterpreted.
Drinking From The Toilet - Hannah Brannigan from Wonderpups training offers up what she calls "a dog training podcast for serious behaviour nerds". She has interviews with some very well-respected people in the world of dog training and behaviour. She has a lovely presenting style, is easy to listen to and relate to, and covers very interesting topics. Her interviews are always fun and relaxed but full of information.
Fenzi Dog Sports Podcast - I was a little unsure of this podcast at first, as it seemed to be little more than introducing the FDSA instructors, but it's grown into something very interesting. Aimed at competitive dog sports, Melissa Breau interviews FDSA trainers about their sports and specific challenges within them, many of which can be applied to real life scenarios with pet dogs.