Okay, there are a few reasons why I'm opening this thread: I haven't slept today because I was reading something absolutely amazing for 7 hours straight (which could make this whole thing a bit incoherent and probably way too long), I think some people might appreciate this kind of more "mature" Manga but maybe haven't heard of good and convincing examples yet and I'd also love to hear other people's recommendations or more Manga in general that fits these criteria. With that out of the way:
Gantz: You may have seen the anime, but trust me the Manga is literally hundreds of times better. The overall story is insane (obviously no spoilers, but trust me on this one) and the fighting scenes and especially the monster design are absolutely superb. Tons of gore and sadly some unlikable characters at first (the MC starts out at 14 or 15 years old, so he's obviously a stupid, horny teenager) and unnecessary and out-of-place sex scenes here and there. Come for the story and the gore and tolerate those 2 things and you'll have an amazing time.
Parasyte: again, there's an anime to this but the Manga is just incredible and definitely worth a read. A likeable MC, a completely unique dynamic between the MC and his "companion", interesting premise and overall good developed story (a love interest that seems to make sense). That combined with very good character development and a good artstyle and monster design makes this another gory masterpiece.
Uzumaki: By Junji Ito, it's classic japanese horror (body transformation and general weirdness) stretched out over tons of seemingly unconnected little stories that lead to a pretty epic conclusion in the end. Insanity and the aforementioned body transformation makes this a pretty disturbing experience, but I loved every single second of it. While we're at Junji Ito's work, Gyo is also pretty good, but can be ridiculous at times.
Sundome: A warning, this is borderline Hentai, so if you're not comfortable with this stuff then forget it. It's a romance/comedy story of 2 teenagers (15 - 17 across the story, strong female lead) which heavily focuses on psychological SM. Complete dependence on the partner, the willingness to completely give yourself up for them, etc. mixed with lots of scenes that many might view as disgusting (all kinds of body fluids play a big role in this, again, a warning if this simply isn't for you). In the end it's an amazing love story and incredibly sweet and romantic at times, with slapstick comedy thrown in every other chapter. It also gets very freaking dark as well. One of my all time favourites. From the same author (Okada Kazuto) there's also Ibitsu, which looks amazing but isn't officially available in english yet.
Ibitsu: (not the one from Okada Kazuto, a different author) Do you want to see a gothic lolita ghost thingy murder people in some incredibly gruesome ways? That's this manga in a nutshell. It's fairly short but a fun read if you want some simple and quick gore and some psychological torment. There are also some quick one shots every 10 chapters or so which have some interesting concepts to then, and the main story has a nice little twist at the end.
Memories of Emanon/Sasurai Emanon: Fairly short but a very interesting little story. A human who has the memories of all its ancestors engraved in their DNA wanders around and just leads a fairly interesting life, affecting the people around her over several generations.
Doubt: Murder mistery, Saw-esque Horror/thriller type of Manga. Pretty cool if you're into that kind of thing, lots of psychological pressure on the cast of characters and a well developed plot that just "works" for this kind of genre. A fun read, nothing too heavy.
Ghost in the Shell: It's freaking Ghost in the Shell, it's cyberpunk goodness and an absolute classic. Lot's of hacking, cyber warfare, shooting and indepth conversations about philosophical topics such as the humanity of cyborgs/enhanced people or if robots could gain a "soul" (a ghost) through some means. It also still looks good to this day and has a pretty nice artstyle.
Akira: Many have probably seen the movie (which is just pure eyecandy) but, as always, the Manga offers a bit more. The story is actually quite a bit longer and you can watch Tetsuo get even more terrifying and insane. More drugs, more violence, more motorcycle chases and a bette story with a proper ending, if the movie intrigued you you should probably give the Manga a try.
Oyasumi Punpun: Weirdness, insanity and psychological trauma meet a slice of life-type of story. You basically just follow Punpun and the people around him from his elementary school days until he's over 20. Basically every character is a complete and total nutjob in this Manga, the style and the visuals are absolutely striking, the story changes from sad to cute to insane and then turns pitch black at some points, the visuals always match what's going on in a really creepy way, and it was an absolutely amazing read. Seriously, you can't talk about the weirdness and the genius of this Manga without spoiling anything, but it blew me away completely. In the end every single character is despicable in some way, but since they all had all these issues and inceidents while growing up you just can't decide whether you sympathize with them or despise them.
Anorexia: Only 2 volumes of a really weird story. Insane rich people, a girl who doesn't want to continue this lifestyle and some random dude who gets entangled in all of this. I personally really enjoyed it but it's just one of those WTF-type stories that just have to click with you, otherwise you probably won't enjoy it that much.