History podcasts I like:

Revolutions. Well known; Mike Duncan goes through various revolutions through history in an excellent, detailed narrative.

American History Too!: two academics from the university of Glasgow have various guests on to discuss different topics from American history. They know their stuff and are really charismatic.

In Our Time: BBC podcast that's been going since the early 2000s. A panel of academics are interviewed and discuss a topic on which they are all experts. Incredibly well researched and interesting, though not especially humorous.