Although I enjoy many many others regularly, this is my short list, my favorite three are at top. What are yours?
*Reply All—I wouldn’t think I’d like this, it’s basically a tech show and I'm not very techy, but it’s often clever/funny as hell and the hosts make it all accessible. Try these episodes: Zardulu, and Raising the Bar.
*Snap Judgement---Usually starts with a personal story from the host, then goes into short vignettes from contributors. Try “Godsend” Episode #614.
*Stuff Mom Never Told You About—Two witty feminist hosts---often hilarious—--with great content. Try “Surfer Girls,” “A Buffer of Whores,” or “The First Lady of the Black Press.”
This American Life—The classic show. Feels a little outdated, but still cranks out great content. Try “The Super” episode #323, or “129 Cars” episode #513.
Serial—-A longform podcast that almost everyone's heard of. Season One was much better than Season two, but this spawned a lot of imitators, and spoofing on SNL: https://www.youtube.com/watch?v=ATXbJjuZqbc
The Black Tapes—A fiction series (or is it???) about a Sarah Koenig-style journalist investigating demon worshipers and the occult. Start at the beginning, it’s very good (and not too scary).
Joe Rogan Experience—It’s not for everyone, it gets a little bro-ey at times, but the irreverent jokes are good and he has on out-of-the-box guests who break down all kinds of things from Donald Trump to space aliens to human performance. Try the recent episode with guest Justin Wren, an MMA fighter who was bullied as a kid and now builds wells for people in Africa, breathing guru Wim Hof, or Abby Martin, a gonzo journalist who loathes American imperialism.
99% Invisible—Fantastic Host, and usually great stories. Their “Miss Manhattan,” show is one of the best podcasts I’ve ever heard. Also try “Mojave Phone Booth.”