Ok, this will take a while to write out. Here we go
There are more than I listen to, but these are the ones that I would recommend completely without hesitation. If it is your thing, then, well... enjoy. :)
If you are interested in history podcasts, I listen to quite a few of them myself, I will come back with a list of good ones.
This is awesome, thank you very much for this. I would probably add Coursera to the Online Education section, and there are also lots of History podcasts of good quality. A good place to start is the AskHistorians podcast, created by the good people at the AskHistorians subreddit, where they interview actual historians about their field of work.