General

I BET You'll like NO GAME NO LIFE also THE WORLD GOD ONLY KNOWS !

Monster - 74 episodes of intense goose chase.
Shiki - Similar concept to Tokyo Ghoul (without the action) but has a deeper meaning imo.
Shinsekai Yori - Plot twistzzzz
Kara no Kyokai series - Confusing at first but gets better. Insane animation (by ufotable) and OST (by Yuki Kajiura)
Grisaia no Rakuen - The last few episodes are worth it.

Shiki

The Legend of the Galactic Heroes.

Selector Infected Wixoss. Looks like a cute card game anime. But hahaha, is it? Subtle.
Fantasista Doll. Also a cute card game anime. Don't really remember what happens. Subtle.
Aku no Hana. Very unique, but I never continued it.
Btooom! Definitely a lot of dark themes.
Princess Tutu. This one is pretty cute too, but each episode starts with a twisted fairytale.

I'm more of a manga person so here's a few:
Kuro (Somato). Also pretty cute.
Dice. (Manhwa/Webcomic) Subtly dark.
Winter Woods. (Webcomic) I really like this one.

Some games (watch some walkthroughs maybe):
Transistor
Undertale
Witch's House
Ib
9-9-9
Dangan Ronpa (There's an anime but it's not as good imo)

Erased,Higurashi,Monster,Death Note,Death Parade

Akame ga Kill

@mmorpg: I just started it. It's pretty great so far.

I also watched Mirai Nikki, which was decent. I watched Shinsekai Yori too, and it was amazing. The reveal at the end blew my mind.

are you watching Erased this season

Code Geass
Guilty Crown
Gundam 00

Your Lie in April

Erased

Gakkougurashi is pretty good it'll leave you like D: at the end of the first episode and Madoka Magica is pretty messed up too.
Higurashi and another are definitely favourites though

Ergo Proxy, Death Note, Deadman Wonderland, Mirai Nikki, NGE, Zankyou no Terror (though it's more thriller imo). For movies, I'd recommend Ghost in the Shell and Paprika

Shinsekai Yori!

I'm kind of a big horror psychological guy myself too lmao. (ahh the ones you listen are so good. well, except psycho-pass, which I can't talk about as I havent seen it yet. Its next on my list )
I'm probably repeating a lot of the ones here, but here we go.

Probably in this order:
1) Mirai Nikki
2) Higurashi no naku koro <ni/kai/rei> (don't bother with kira, iirc it just becomes ecchi comedy)
3) Death note
4) Shinsekai Yori
5) Death Parade
6) Another
7) Deadman Wonderland

That should leave you with a lot to watch for now I've got more if you need lmao

Higurashi(seems like a slice of life at first, but then....)
Another

elfen lied was so gore-infested and bloody and terrible but i still loved it i watched it when i was like 13

try "another". you've probably heard of it, it's like really unsettling and unexpectedly dark for such a cute-looking art style. it's not really scary in my opinion at times but it kind of keeps you at the edge of your seat

My Little Pony: Friendship is Magic. It's very dark and psychological, in more ways than one.

@hoboscanfly: Yooo Lain is amazing, great pick.

OT: Ghost in the Shell is my recommendation. Its so freaking good (start with the original movie, its great).

Battle Royale is pretty good.

I highly recommend Shinsekai Yori and Rainbow: Nisha Rokubou no Shichinin.

Darker than Black.

Higurashi
Cory in the House

Higurashi no naku koro ni
Another

Future Diary/Mirai Nikki

I guess if you like trash like Elfen Lied, you might also like Gantz...

serial experiments lain

we bare bears

Death Parade is one of my favorites, quick summmary taken from MyAnimeList
After death, humans are either sent to the void or reincarnated. But for some, at the instant of their death, they arrive at Quindecim, a bar attended by the mysterious white-haired Decim. Since guests do not initially remember their deaths, Decim tricks them into playing games with their "lives" on the line, with the secret intention of drawing out their true character to judge them.

Shinsekai Yori
Death Note
Infinite Ryvius
Speed Grapher