>>991349Apart from Ghibli Movies, also Satoshi Kon Movies, like Perfect Blue and Paprika.
Original Ghost in the Shell
Akira
Angel's Egg
The Girl Who Leapt Through Time
In This Corner of the World
Kotonoha no Niwa
Appleseed
Cat Soup
...Most movies that aren't part of a series should be fine, really.
As for anime series...
Serial Experiments Lain
Kino no Tabi (I've only seen the 2003 version, so idk whether the new one is the same)
Berserk (1997)
Mononoke (not the ghibli movie)
Paranoia Agent
Cowboy Bebop
Hunter x Hunter
Erased
NHK ni Youkoso
Monster
Darker than Black
Kiseijuu: Sei no Kakuritsu
Death Note
Trigun
Fullmetal Alchemist Brotherhood
Angel Beats
Michiko to Hatchin
Samurai Champloo
Baccano
Sayonara Zetsubou Sensei
Mecha, but maybe also The Vision of Escaflowne
Banana Fish
Barakamon
Usagi Drop
Tsuritama
OreGairu
Wolf's Rain
Devilman OVA (The birth 1987 and demon bird 1990) (manga is better)
Devilman Crybaby (is kinda different from the original manga)
Detective Conan
Tiger & Bunny
...I'm really not as sure about those last ones, but they might fit the bill as well.
Also I'd recommend checking out the ones I put higher on that list first.
Hunter x Hunter might seem like a typical shounen at first, but imho it gets better the more you watch.
Also probably these, althogh I haven't actually watched them yet:
Shigatsu wa Kimi no Uso
Higashi no Eden
Ergo Proxy
Texhnolyze
Legend of the Galactic Heroes
Haibane Renmei
Mushishi
Steins;Gate
Dennou Coil
Vinland Saga
Shoujo Kakumei Utena
Shouwa Genroku Rakugo Shinjuu
Eizouken ni wa Te wo Dasu na
Uchuu Kyoudai
Hyouka
The Tatami Galaxy
Ping Pong the Animation (It's sports but I heard its really good)
Bakuman (Only watched a few episodes and I really hate this one, but I guess there are people who like this)
If you ever feel like watching something truly horrible then Chargeman Ken, other anime will look good in comparison.
There's more in picrel, just watch whatever catches your interest.