If you'll forgive the lack of originality, I've previously given my own recommendations here. For convienence, here they are again with minimal editing and extra shilling:

We had a recent post on recommended podcasts, whose recommendations echoed a similar post a couple years ago.

First, support your local casters:

• The AskHistorians Podcast: At around 1-1.5 hours per episode, you could easily power through these in week, if you forgo most of your other waking activities. Godspeed and good luck. Of note, I am the host and producer of the podcast, so if you have any questions about the show, feel free to ask. Past discussion posts can be found here.

• /u/bemonk has, I think, 8000 different podcasts out right now? History of Alchemy, Germany, Bohemia. Check here.

I'd say the recommendations that come without, or with little, qualifiers would be:

• A History of the World in 100 Objects: Director of the world's largest crime scene (i.e., the British Museum) describes objects and their context. Sounds dull in concept, but is absolutely mesmerizing.

• In Our Time: Professional curmudgeon Melvyn Bragg interviews a trio of (usually British) academics on a particular topic. This is actually one of the inspirations for the AskHistorians Podcast.

• Backstory: A trio of US History professors cover a particular topic or theme. Actually a radio show, so there's a segment where they take (curated) calls.

• Duncan's The History of Rome and Revolutions. THOR has kind of become the gold standard of amateur history podcasts. Revolutions continues that quality.

Frequent recommendations, but with caveats, are:

• Hardcore History: We've got a love/hate relationship with Dan Carlin around here. He even has his own FAQ section.

• Stuff You Missed in History Class: kind of a shallow approach, and definitely dependent on who the hosts are (the current pair are probably my least favorite). Also, rarely goes outside white people history.

• Lar Brownworth's 12 Byzantine Rulers: our own /u/shlin28 gives a critique and counter-recommendation for Pierson's History of Byzantium. Brownworth also has a Norman Conquests series.

Some other frequent mentions that I don't know enough to comment on, mostly amateur single focus productions: The Ancient World, The China History Podcast, Short History of Japan, Russian Rulers.

Adding to this list, I recommend the 15 Minute History podcast out of UT-Austin. It features quick interviews with academics on their topics of interest.

Both of Mike Duncan's podcasts, The History of Rome and Revolutions, are superb.

When Diplomacy Fails is another good podcast. They go through the causes of major wars. Last year they did a day-by-day episode of the July Crisis to mark the centenary.

There's a new podcast called Our Fake History that has been pretty good through ten episodes. A guy basically discusses historical myths, where they come from, and what the real story is.