I don't have any particular noises I turn on to fall asleep, though I do find I sleep better when my cat's in my bed with me. This could be attributed to her purring but... it probably has more to do with me being more inclined to move around a lot as I try to get to sleep because I feel bad waking her.
I'm the direct opposite of many in that I absolutely can't sleep with a fan on (which is great in the summer). The kind of constant, unchanging sound like that and white noise is honestly hell for me, right now there's some ventilation thing in my apartment that often starts making noise when I'm about to go to sleep so then I need to put something on to cover the sound. Usually someone talking, like some let's play or a podcast (basically all I use podcasts for).
For the most part I don't need complete darkness, and going to bed as the sun is rising outside can be pretty chill.
A good rain helps me fall asleep. I hafta have my fan on these last few years, not because of white noise but because some of my neighbors are turds who think it's cool to rev their loud obnoxious motors at any hour of day or night. So I need a blocker.
Generally, I gotta have complete silence & darkness, but there's night where my tinnitus is so dang bad I gotta have some sounds. I'm also a heinously light sleeper, so I wake very easily to noises & never really have been able to shake that my entire life. In those cases I can only hope that it rains, or something, as that doesn't wake me up for some reason. Fans are a bit too buzzing for me (too much like my tinnitus) & listening to music tends to give me intensely bad dreams for whatever reason. Rain's generally my best friend. My partner ALWAYS sleeps with headphones in & listens to podcasts of all things, & sleeps like the dead. I'm so jealous of it or anyone who can sleep to the sound of voices.