Oh my god yes - all podcasts, all the time!
I listen to Welcome to Night Vale, like half the population of the internet, and I love it to pieces. However, I mostly tend towards history-themed podcasts. I used to listen a lot to Stuff You Missed In History Class, but I've kind of stopped. Not because the pod is bad or anything - it's pretty dang excellent! - it's just that I prefer my history in larger chunks, with more context than they have time to give in one or two episodes, so I tend more towards narrative-form history-pods these days.
My current history-pod listening list:
The British History Podcast - the story of England, from the bronze-age onwards. The goal is to make it to World War II, and then stop. At 160 episodes, he's just made it to 800 AD. He spent 33 episodes on Roman Britannia alone! <3
History of Rome - speaking of Romans, Mike Duncan's podcast on the rise and fall of the Roman era, from the founding of the city of Rome to the fall of the Roman Empire in the West in the 400s AD. So many wars, so many political feuds, so many insane emperors!
History of Byzantium - continuing the Roman theme, Robin Pierson picks up where Mike Duncan left off, continuing the story of the Eastern Roman Empire, with the intent of making it all the way to Constantinople's fall to the Ottomans. Right now they've made it to Emperor Leo and the iconoclasm!
Revolutions - after Mike Duncan finished up his story of the Roman Empire, he moved on to the topic of revolutions. He's gone through the English revolution and the American revolution, and is now mired neck-deep in the French revolution.
History of Philosophy (without any gaps) - taking a sidestep away from the kings and wars and politics-kind of history, the History of Philosophy podcast does exactly what it says on the label; it tells the history of philosophy, listing not only important philosophers, but also giving explanations for their philosophical ideas, and does a good job of covering not only the ancient Greeks and their later heirs in medieval Europe, but also traces philosophy in the Islamic world. Will be getting a separate spinoff pod about Indian (and Chinese?) philosophy.
History of the Crusades - a finished pod about the Crusades! Narrates not only the crusades themselves and what happened in the Holy Land, but also gives the wider context, detailing European power politics and religious and political conflicts in the Muslim world pre-, post- and between the individual crusades.
... and that's about it for now. I've got some other podcasts on the list that I haven't had time to listen to myself, and therefore don't feel comfortable recommending them.