Criminal is probably my favorite true crime podcast. I also listen to Someone Knows Something, which tells a cold case story each season. Both seasons of Serial were also really good.
For other true-life podcast recommendations, I'd go with This American Life, You Must Remember This (which tells stories of Old Hollywood), Unladylike (from the former hosts of Stuff Mom Never Told You), BackStory (the hosts take topics currently in the news and delve into their history), Dear Franklin Jones and Heaven's Gate (which both tells stories of cults), Science Vs (which takes a topic and explains the science behind it), Stuff You Missed in History Class, and Stuff You Should Know. If you're a fan of the musical Hamilton, listen to the HamilCast. I also really like Dan Carlin's Hardcore History, but that one isn't for everybody, since episodes are few and far between and tend to be really long (the last one was over 5 hours).
If you want something more supernatural that pulls from real-life events, try Lore or Unexplained.
For fiction podcasts, my favorites are Welcome to Night Vale, TANIS, PleasureTown, and Thrilling Adventure Hour (which is now mostly defunct). Welcome to Night Vale and TANIS are both very much in the sci-fi genre, and PleasureTown has an old-western type feel.
(sorry, I listen to a LOT of podcasts!)