For me it's really just down to the fact that it's just wonderful escapism. I love that I can pop in any random episode and just wrap myself up in that Twin Peaks mood. The atmosphere is definitely the thing that does it for me, a sort of synthesis of the warm color scheme, the camerawork, the pacing, the lighting, the clothes, the locations, the strange off-kilter dialogue, and, most importantly, the music. It really doesn't matter which storylines are going on; it's the sensuous, dark, dreamy feel of the show that always brings me back. I hear the first strains of Angelo's theme and BAM, I just feel completely transported into this strange little fairy tale world that exists in a corner of Washington State. And the imagery and audio (dialogue, music, etc.) are just so beautiful to me, more so than any other TV show.
I also think that part of the reason Twin Peaks has stayed alive so long in the fan community is because there so many dangling loose ends, it gives you so much "room to dream," as David Lynch likes to say. Who was the shadowy figure lurking behind the tree when Bobby met Leo in the woods? Why were people's hands shaking in Episode 27? Who survived the bank explosion and who died? What's going to happen to Coop? And how's Annie?? We'll never know, and in a way that's wonderful because we'll always have something to talk about!
I also kinda like Twin Peaks because it feels, in a funny way, like my little secret to share. Most of my friends were really too young to get into it when it was first on and never saw it (or only have vague recollections), so there's nothing I love more than sitting them down and showing them the pilot and seeing their reaction to it. It's not like Friends or Seinfeld, which everybody and their mother has seen. Twin Peaks feels like a special experience I can share. And because it's so unique and original, it always prompts good conversation afterwards because everybody reacts so differently to it. And it's sooo satisfying when they start begging to borrow the episodes in rapid succession and begging you to give a hint as to who the killer is...
So yeah, sorry to be long-winded, but like you said, it's a lot of things! It's scary as hell, hilariously funny, completely absurd, deeply moving, sexy, romantic, and usually all of those things at the exact same time. How many other TV shows can claim that?