Serial Experiments Lain is everything wonderful about anime. It is violent, dark, scary. In summary: ADULT. Anime tells stories in a visual format that for years and years you simply could not get anywhere else. Adult genre fiction was not well represented in American media. Even today, adult American cartoons are almost entirely "sitcom" format. They don't want to ever end, and they do not want to tell a story, they…
Have any good adult animes come out these past few years? There's always been a lot of gross stuff but I'm starting to lose faith in the medium when I see stuff like Mushoku Tensei being praised as wonderful in the mainstream, the latest few seasons have felt like complete garbage.
Puella Magi Madoka Magica if you're into Anime-deconstructing-Anime. "What if Magical Girl... but actually, when you think about it that's entirely horrifying". There've been a bunch of other attempts at similar things, usually not as successful.
Vinland Saga for heightened, violent historical drama.
Mushishi if very-very-Japanese things aren't a turn-off. Largely episodic series about a guy who deals with dangerous spirits. Which I know reads like it'd be terrible or "oh my god not another one of these shows", but it's not. Slow-paced, brooding, bittersweet.
Anohana: The Flower We Saw That Day. Short slice-of-life series about kids, but actually about accepting loss. IDK how "adult" it is, but it's pretty good (I mean actually-good, not anime-good).
Carole and Tuesday. Again, not sure how "adult" it is but it's just charming and heartwarming, while also not being terrible, which is a rare enough combo in any media to be worth a look, I'd say. From the creator of Cowboy Bebop, and also heavily music-focused.
May not look like it from this list, but I don't actually watch that much anime. I know there's a fair amount of really good stuff I haven't seen, plus a huge pile of OK-but-not-great. I keep up with a couple ongoing series I didn't put on this list because they're definitely not aimed at adults (My Hero Academia, for instance). I find it's really hard to find good recommendations for anime unless they're personal recs from a person I know well—but I also find that's true of most other genre-fic sorts of things. Recommendations from Internet randos or "best-of" lists of fantasy are often (IMO) full of garbage, and sci-fi's barely better. Ditto comic books.