I'm a big history nerd, so…
The History of Rome: A fantastic 100+ narrative episode podcast that tracks Rome from its founding to the establishment of its empire, the fall of its republic, and ultimately the fall of Rome itself.
Revolutions: Hosted by the same guy as History of Rome, each season of this podcast tracks a different revolution in world history (think American Revolution, French Revolution, he's currently in the midst of the Russian Revolution). The season on the Mexican Revolution is my favorite single season of podcasting anywhere.
Dan Carlin's Hardcore History: This is for the big deep dives on major sagas from history. Like 5 episodes on the Mongol invasions, or 6 episodes on WWI. Dan Carlin's delivery and depth is great. I know I've seen threads on this show here before. Older episodes cost $ to download, but it's a fantastic show.
Abridged Presidential Histories: Shameless plug - this is my show. Every episode looks at the scandals, setbacks, and successes of a different president's life and administration, in chronological order, in 60 minutes or less. I also added interviews with historians a year ago (starting with Buchanan in the chronology). Latest episode is about McKinley, TR is up next. Fair warning, Texags, I'm a liberal progressive. I'm not going to bash you over the head with it, but it might be triggering to some when I talk about gilded age income inequality or our historic treatment of slaves and minorities. If that's going to bug you, probably not the show for you.
Thanks and gig'em