I actually think this is a bit tougher than it sounds because of how broad cogsci is as a field. Not too long ago, I asked a similar question on twitter; to this end, here are the podcasts that I now regularly follow:
99% Invisible - A show about design, and the factors influencing it.
Lexicon Valley - Covers language from "pet peeves, syntax and etymology to neurolinguistics and the death of languages".
Brain Science Podcast - Mentioned in another answer. The host's in medicine, but the show discusses neuroscience and ow our brain makes us who we are.
Very Bad Wizards - One of my favourites. The product of a psychologist and a philosopher, sharing a marked inability to distinguish sacred from profane.