If the question is off-topic, not constructive or opinion based, please let me know and I will delete it.
Here are the ones I know about; there's much more about neuroscience than, say, theoretical or computational cognitive science, but a lot of the neuroscience podcasts cover cognitive science indirectly or partially.
All in the Mind--it's also neuroscience and mental health stuff (a lot of mental health stuff)
Brain Science Podcast--books about and interviews with researchers in neuroscience
Neuropod--Nature's neuroscience podcast
Neuroscene--"the future of neuroscience", mostly interviews or topical explorations
Naked Neuroscience--the neuroscience offshoot of Cambridge University's Naked Scientists
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.
I enjoy Brain Matters, it's very neuroscience based & full of interesting people