One of the most influential cultural figures in my (part of) my world is Mike Duncan. Duncan pioneered a deeply researched, perceptive, snarky style for presenting longform history podcasts in the History of Rome, and then in Revolutions.
The first history podcaster with a high profile was probably Lars Brownsworth with his Twelve Byzantine Rulers, many years ago, but I think it took Duncan to really show how a regular person, working hard, could do it.
Robin Pierson, with his imposing The History of Byzantium is the most obvious successor, since he took up where Duncan left off, with the intention of going all the way to 1453.
But lately I've really liked The History of the Twentieth Century by Mark Painter, who, from his biography, also writes science fiction. No wonder it's good. He picks interesting music of the period (he had a particularly funny run of playing "A Hot Time On The Old Town", which seems to have been the sound track to America's introduction to overseas military intervention. He really seems able to pull out the interesting and significant points from any incident, character, or situation. I'm a big fan.
Many podcasts are self-indulgent, unedited, and focused on whatever happened in the last five minutes. I like a couple of those (like the Slate Political Gabfest and Slate Money). But, by and large, it takes a lot of work and editing to get a podcast worth listening to.
I'd love to do a podcast myself, but have trouble getting done what I need to already. I have a concept, topics, and everything. Someday, maybe....