Just Anime

I admit, this is my first post here on anime vice - I found this site via GiantBomb and whiskey media in general. I wanted to start this topic on GB, but I figured you guys here know better.
 
I'm going on a week trip in the near future, and I've been wondering if you guys here know any anime series (preferably short) which could fit my taste.
 
Animes I enjoyed:
-Elfen Lied
-Dragon Ball
-Evangelion (nearing the end now)
 
Animes I don't like:
-Naruto-ish
-Bleach-ish
-One piece-ish
 
Animes I loved:
-Death Note
-Kaiji: the Ultimate Survivor
-Akagi
 
I admit I haven't watched many anime series, but that's mainly because I have no idea which ones to pick. I love animes (and movies, and tv series) that are more psychological and based on you going WHAT THE?!? every single episode. I don't like animes based on epic fights, and I hate the ones that are supposed to be "japanese funny", with 12 year old girls dancing and having these awful cat-like expressions... with their... hands... raised like... paws... yuck.
 
So if you know any animes with incredible plot twists and mindfucks, I could use your expert opinions.
 
Any help will be mucho appreciated.
 
PS.I prefer animes that have a single, developing story throughout the whole series (eg. Death Note) over the ones where every episode tells a single short adventure (eg. Pokemon).

@imsh_pl:
Hm, short anime? How short exactly?
I can list you a few 12-13 episode long series but I don't know what you consider short.
Though I read you're in the middle of watching Evangelion. Well, the ending is damn confusing there. I recommend you to watch the End of Evangelion movie straight after finishing the TV series.:)
It's essentially an alternate(more epic) retelling of the finale. If you've watched the entire Evangelion series then you sure gonna understand it.
 For plot twists, dark atmosphere and gorry action I advise you to watch Kurozuka

Kaiba and School Days come to mind.  What did you like about Dragon Ball that you didn't like about Naruto, Bleach and One Piece?

Big O is a definite short anime and it is damn kool too if your into the whole james bond type bruce wayne giant robot saver of the city thing. Or perhaps Zone of the Enders

Perhaps I should rephrase myself... the anime doesn't exactly have to be short. My priority is the psychological aspect.
 
Thanks to anyone who posted, feel free to add more suggestions.

I dont have watched all these animes. Some are indications from friends of mine
 
For really short animes these are good
 
[5 epis] Golden Boy >>> Comedy + Ecchi (Really funny)
[4 epis] Cobra the Animation: The Psycho-Gun  >>> Action + Sci-Fi (reminded me of Cowboy Bebop)
[6 epis] Karas >>> Action + drama (Looks like a animated tokusatsu)
[7 epis] Freedom >>> Sci-Fi + Space
[8 epis] Bokusatsu Tenshi Dokuro-chan >>> Comedy + Ecchi + a lot of blood XD

For anime with average 12 epis
 
[11 epis] Higashi no Eden >>> Romance + Mistery + Drama
[12 epis] Kami nomi zo Shiru Sekai >>> Romance + Comedy (It's really god for a romantic shounen)
[12 epis] Sayonara Zetsubou Sensei >>> Comedy
[12 epis] Ga-Rei: Zero >>> Action + Drama + Supernatural ( Must See)
[13 epis] Panty & Stocking with Garterbelt >>> Comedy ( Must See)
[12 epis] Detroit Metal Ciry >>> Comedy + Music ( Must See)  
[12 epis] Boogiepop Phantom  

For animes that are "shorts"
 
[12 epis] Detroit Metal Ciry >>> Comedy + Music ( Must See)
[39 epis] Higepiyo >>> Comedy
[13 epis] Panty & Stocking with Garterbelt >>> Comedy ( Must See) 
[8 epis] Bokusatsu Tenshi Dokuro-chan >>> Comedy + Ecchi + a lot of blood XD
 
For the psychological genre
 
[22 epis] Shiki
[24 epis] Gankutsuou ( Must See)
[23 epis] Ergo Proxy
[Movie] Akira
[Movie] Kara no Kyoukai (Watch all 7 movies)
[12 epis] Sayonara Zetsubou Sensei
[12 epis] Ga-Rei: Zero  ( Must See)  
[11 epis] Higashi no Eden
[Movie] Millennium Actress
[Movie] Paprika
[Movie] Perfect Blue
[24 epis] xxxHOLIC
[74 epis] Monster
[12 epis] Boogiepop Phantom 
[24 epis] Welcome to the NHK! 
[Movie] Mind Game
[13 epis]  Serial Experiments Lain

@lafeier: Yep, I enjoyed Perfect Blue, and want to watch Paprika as well.
 
Thanks everybody for the advice!

@imsh_pl: I only watched Millenium Actress from satoshi, but i have Paprika here. Im going to watch it today =]
 

If you like psychological animes, I'd recommend Ghost Hound, Monster and Ergo Proxy!

@imsh_pl: I second Ga-Rei Zero. It's great. Not exactly what you are looking for but the story is very engaging.
Ergo Proxy is nice too. You should try it. Cyberpunk anime with some deep questions.
Higashi no Eden: lighthearted Death Note with cell phones. Watch the movies after the series!
Monster: yeah, etalon. Johan Liebert is a legendary villain. Bit too long(70+ eps)
 
More later.;)

I don't really watch much anime but there a few i enjoyed. 
 
Tokko -  Shindou Ranmaru has just graduated from police academy and assigned to Tokki: Special Mobile Investigation Force. On the day of his graduation, he meets the half-naked girl he has been seeing in his dreams, Rokujo Sakura. It turns out she works for a secret group within Tokki, known as Tokko: Special Public Safety Task Force. Shindou ends up joining Tokko to avenge his parents' death, and solve the mystery mass murder of residents in his hometown of Machida. Bottomless pits start to appear around Japan, and mysterious creatures emerge from them, linked to the mass murder of humans. All this to do with something called "The Box of Dirge".  
  
Seikon No Qwaser  -  The story takes place on the grounds of St. Mihailov Academy, a Japanese Eastern Orthodox school, and draws heavily on religious references from the aforementioned religion. Here it follows the trials and hardship of two of its students, Oribe Mafuyu and Tomo Yamanobe, until the encounter with a mysterious, silver-haired, Russian boy named Alexander, or Sasha for short. This pits them and the whole school in an all-out war between the Church itself and the so-called "Adepts", a sect of individuals wielding powers linked to the elements of chemistry. 
  
Shinrei Tantei Yakumo  -  Shinrei Tantei Yakumo, aka Psychic Detective Yakumo, tells a story about a college student, Saitou Yakumo who is born with different eye colors. His red left eye gives him a special ability to see ghosts and spirits. He believes ghosts and spirits are bound to earth because of a certain cause, and simply eliminating that cause will let those spirits rest in peace. Being asked for help by Ozawa Haruka, they begin the investigation together. 
 
There are a few others such as 
Soul eater
D gray man
Helsing 
Fairy tail 
Those are fairly long anime's. 
 
Gore~