This post is in now way, shape, or form insulting the podcasts I list below (I'm not saying they're boring, because they aren't!) But as someone who has had insomnia that ranges from wretched to occasional-but-mild, I'm willing to do pretty much anything that gets me to sleep. Normally reading can wind me down, but sometimes that doesn't work.
What does often work for me: listening to certain types of voices speaking in particular types of ways. These are some of my regular podcasts I listen to--on very light volume--when I'm trying to get to sleep. Typically I use the my sleep timer on my phone on for one hour, then it automatically turns off.
1. Reveal
My top choice. This podcast is from the Center for Investigative Reporting, which does fantastic in-depth stories on important issues. Two recent really good episodes were about racial disparities in lending for mortgages and one on a contraceptive implant and how a company and the FDA responded (or didn't respond..) to serious health issues it caused. The host has a soothing, smooth voice, and there is never any abrupt music or sharp sounds (loud laughter, etc.)
2. Generation Why
This one may overtake Reveal as my favorite. Not good if listening to stories about murder disturbs you.. so disclaimer there. Each episode focuses on a murder or serial killer. The two hosts handle the content from a research angle that is dead serious (no jokes) and they clearly do a lot of research for each episode. Both the hosts have incredibly soothing voices and both, weirdly enough, happen to talk with this rhythmic cadence that just lulls you.
3. Teen Creeps
I wish I had discovered this one sooner. The two female hosts are comediennes/ writers who read one teen YA pulp horror novel a week and rehash it on the podcast. I was a huge reader of Christopher Pike and RL Stein-- both of whom are strongly represented. I had fond memories of these books, but boy do they not age well. They rehash the plot but also provide commentary and go on tangents. There is some laughing (quite a bit, actually), but no music or abrupt noises. You don't need to have read the books to follow the podcast. They both have softer Millennial-ish voices that never bother me.
4. Here to Make Friends
So yeah, this is a podcast about the Bachelor franchise. (They cover both the show and all its spinoffs). Which of course means it's only running when there is a current show, with a new one released about a day after each airing of the show. The show approaches the Bachelor from exactly the same perspective I have on it: it's ridiculous, but often riveting.
5. This American Life
Only the non-humorous episodes, which occasionally have weird sounds. The ones that cover only one story per the entire hour are best. Just to note that there is some music which occasionally pops up.
6. Someone Knows Something
This Canadian podcast covers one incident for an entire season, doing a deep dive into murders and disappearances. It's soothing and understated, never intense despite it's content.