I always recommend the BBC's In Our Time. A panel of experts, usually university professors, discussing their topic with the host for a lay audience. Plus, if you find Rome boring they have a huge back catalog of history, literature, science, religion, culture, music, etc. http://www.bbc.co.uk/programmes/articles/2Dw1c7rxs6DmyK0pMRwpMq1/archive

There's an official /r/AskHistorians Podcast, and it's pretty good!

That depends on what history you are actually interested in learning, Podcast Ain't Played Nobody is perhaps one of the best ones out there that helps contextualize College Football as it is today, and Bill Connelly is one of the best numbers guys in the business.

While Shutdown Fullcast does the same with more memes and shit posting.

If it's Rome and not Mike Duncan that you find boring, try his other podcast, Revolutions. The first series is on the English civil wars, and frankly I found it pretty confusing, but I feel he really rounds into form by the 3rd series, the French revolution.

History of the Crusades podcast, the host is a little too sing-songy but informative

History of Europe podcast is pretty good too if you don’t mind old man voice with a slight speech impediment

In addition to In Our Time, the New Books in History is one of may favorites for getting at special topics and staying abreast of current historiography. Sean's Russia Blog has a lot of good interviews for Russian/Soviet history. Although its search function is terrible and its name could invoke Archer's phrasing, Backdoor Broadcasting has a lot of good stuff from the UK humanities scene. The London School of Economics podcast and lectures likewise suffers from a poor search function, but has some real good lectures on the past if you can find them.

A few more recommendations: Missed in History is a solid, short overview of people, places, and things often overlooked in history curriculum. Their catalogue is very extensive and wide-reaching.

DIG History and Footnoting History are hosted by historians and cover a range of topics.

UnCivil is new but is doing some really interesting stuff with myths and tropes of the American Civil War and how they relate to modern America, especially for Black Americans.

Ben Franklin's World not only does solid content but does a number of episodes on how historians work, think, and approach a topic or task.

Sexing History is also new and looks at the history through the lens of gender and well... sex.

Finally, Sects Ed looks at religious sects throughout history. They're still finding their groove but the content is really interesting.

Happy listening!

I'm a huge fan of The History of China, and the host is a flair here. History of the English Language is fun for word nerds like me. The first two series of The Ancient World are really great too. (The current series is fine, but it's all about Imperial Rome)

Wittenberg to Westphalia has yet to get to the wars of religion that it is ostensibly about, but it takes you from late antiquity and shows how the roots of the early modern period actually stretch back farther than you might have thought.

It's not history related, but I'm just a big fan of The Splendid Table. Food podcast that has been on the air as a radio show for over 20 years. It doesn't make a lot of sense to listen to this one from the beginning, though.

Side question: for the layman, how do audiobooks compare to podcasts?

There's a few history podcasts that haven't been mentioned that I would recommend:

15 Minute History: similar to the askhistorians podcast in that it interviews historians over a specific subject in their research or expertise. the episodes are shorter and less frequently released though.

New Books Network: interviews with academics over their most recent monographs. They have one for history in general, and also some for other disciplines, some which overlap with history and others that do not. I recommend checking out New Books in Military History as well.

Age of Napoleon: this one isn't done by a professional historian, but by a hobbyist with incredible knowledge. the podcast has a lot going for it. it's paced well and its episodes are mostly organized thematically and chronologically. it also covers the social, political, and military history of the events side by side, so you get a pretty holistic picture of it all.

I really enjoyed A History of the World in 100 objects by the British Museum. It's over now, but still available I think.