Looking for suggestions - help me!

[OtherOne]

So I have seen a lot of anime series and I am frankly running low on ideas. Some of my favorites are (including favorite characters):

Hunter x Hunter (Killua and Hisoka)
Tokyo Ghoul (Kaneki and Uta)
No Game No Life (Sora, Shiro, and Izuna)
Darker than Black (Hei and Wei)
One Outs (Toua)

I tend to avoid romance, hentai, and ecchi but I'm not completely against them if it's not the soul purpose of the anime. I like psychological anime the best. Also if it's a well known anime I have probably seen it: Bleach, Fairy Tale, One Piece, Death Note, Naruto, Fullmetal, Kuroshituji...etc.

Some other anime than I have seen and enjoyed are: Parasyte, Togainu no Chi, Get Bakers, Imawa no Kumi no Alice, Akagi, Jormungand, Monster, or Denpa Kyoushi.

[Kotohono]

I like psychological anime the best. Also if it's a well known anime I have probably seen it:

Just in case I'll suggest these as whats considered well known on Animesuki might not be considered well known for others.
Mahou Shoujo Madoka★Magica & Steins;Gate are two of the best series for this genre & despite their popularity & critical acclaim here & else where I am not sure they're considered well known. Both are very well written compelling series from the genre.

I'll also suggest Mawaru Penguindrum, though it gets a bit too psychological for some people as Ikuhara Kunihiko takes it to another level with symbolizing, and depth of it & abstractions of it at times, it's an excellent series if you can enjoy his style of writing, and if you do I'd suggest Revolutionary Girl Utena & Yuri Kuma Arashi his two other major works that are on a similar level in terms of psychological content while being slightly weaker in terms of storytelling & other aspects in my opinion. But be warned it's not for everyone.

Shinsekai yori & Psycho-Pass two excellent series with psychological elements & two wildly different views of a supposed future utopia, both are very well written & not near on the depths of psychological level that Penguindrum delves to.

Finally, I'll suggest Zankyou no Terror as psychological series about two teenage boys whom turn domestic terrorist & despite being created by the creator of Cowboy Bebop it's remained a relatively lesser known series.

[kitten320]

Seems like you are more into slightly darker action and mind games so let's see:

Akame ga kill
Aoi Bungaku Series - not action but a set of psychological stories.
Baccano!
Berserk
Claymore
Boku dake ga Inai Machi
Code Geass
Fate/Zero
Death Parade
Denpa-teki na Kanojo
Ga-Rei: Zero - Will you kill someone you love because of love?
GTO - comedy but kinda psychological
Hakuouki Reimeiroku - not fully sure but I would recommend to give this prequel a go. If you like it, you can watch 1st season and the rest. In my opinion prequel is better.
Ghost Hunt - I think you might like main character.
Kyougoku Natsuhiko: Kousetsu Hyaku Monogatari
Madoka Magica
Mai HiME - light hearted at first, get more serious in second half. Madoka seems to be inspired by this.
Monster
Phantom: Requiem for the Phantom
Psycho-Pass
Rainbow: Nisha Rokubou no Shichinin
Shiki
Shingeki no Kyojin
Shinsekai yori
Steins;Gate
Zetsuen no Tempest

You probably watched most of them but there still should be enough to keep you busy.