The great thing about podcasts is that there is something for almost anyone. Here are some of the podcasts I listen to, sorted by how quickly I devour the episodes: - 99% Invisible: A+ podcast about all kinds of designs, from flags to buildings to submarines. Almost never fails to pique my interest. - Radiolab: Great stories, amazing audio design. Headphones recommended! I was introduced to Radiolab with the Speed episode. Perhaps the memorable episode I ever listened to is Bliss. - Song Exploder: Pulling apart songs with the composer's commentary. If you know the songs, they're great episodes. For example, Game of Thrones or House of Cards themes. - This American Life: The elephant in the room of podcasting. Has some amazing episodes. Lately they've been doing a lot of reruns and some 'meh' episodes, but they have a huge archive of great episodes, like Death and Taxes - Invisibila: only one season but off to a great start. I found How To Become Batman very intriguing. - Dan Carlin: Hardcore History episodes are basically free, small audiobooks about an aspect of a period of history. I know that doesn't sound appealing, but Carlin is good enough to make anything interesting. His Common Sense podcast discusse about current event from a geopolitical / historical point of view. - The Bugle: John Oliver and Andy Zaltzmann discuss the week's news with humour (much funnier than Last Week Tonight, if you ask me). They're currently on a break, but you can listen to the last regular episode, 291, here. - The Gist with Mike Pesca: episode every weekday, where Pesca opines on / discusses important news and good articles, often with authors or experts. I don't listen to all of what he has to say but he almost always has interesting points (if he's not being silly). Latest episode is quite representative. I also listen to Cortex and Hello Internet, but almost entirely because I like the hosts. Start from the first episodes, it doesn't get much different than that to be honest. edit: I forgot to directly address your question, whoops. My ideal podcast is either thought-provoking, emotive or funny, and preferably a combination of the three.
I would like to make the case for History on Fire with Daniele Bollelli. He's only a few episodes in but I'm impressed by the quality of the show. He just did an overview of the Roman slave wars, and it was really entertaining. I fact checked some of his more.... interesting claims and he had primary sources supporting most of them, to one degree or another. He's also from Italy and I think his first hand knowledge of the geography provides an interesting perspective. Note* there is a hint of try-harding to snag some of the Hardcore History audience.