Animes (not mangas, unless they're exceptional) with a few requisites
 

Ok, I'm looking for an anime with at least a few of these characteristics:

1) Powerful (strong/smart) main character
Vash the Stampede, Trigun
L, Death Note
Alucard, Hellsing

2) Evil (or simply "not good") main character.
Alucard, Hellsing

3) NOT fight-oriented, which means I want to avoid fights for the sake of fighting, such as:
Dragon Ball
Yu Yu Hakusho
Fairy Tail

4) Good character development; Conversation-oriented
Spice and Wolf
Bakemongatari
Katanagatari

5) Mind games
Death Note
Mirai Nikki

A few that I've seen and didn't like or not interested at moment:
School Days (I don't want a soap opera >.>)
Chaos:Head (the main character is more annoying than the regular stupid main character)
Higurashi no Naku Koro ni (tbh, I've only seen one video on youtube about it, the nail removal scene. I definitively don't want to watch this one)

Of course I don't want animes that fits ALL of these categories, since it would be weird having Alucard in a conversation-oriented anime (although it would be interesting).
The first category is the least required. You can completely ignore it if it makes the "search" easier.
I'm really looking forward for the second, though.

I really appreciate any help you guys offer. Thanks in advance! :D

Evangelion had great character development. I'll edit this post when I can think up a few more good ones.

Don't know what you've seen already, but from just last year you should see Steins;Gate, Madoka Magica, and AnoHana. Also check out the currently airing Sword Art Online and Hyouka if you haven't yet.

I'd say all of those fit at least 4/5 of your criteria.

I strongly second Steins;Gate and Madoka Magica. And Sword Art Online definitely fits so far, but it's early in the series.

Fate/Zero and Mawaru Penguindrum(though why this one fits won't reveal itself right away, and I'd rather not spoil it for you) would definitely be another good choices that fit most of requirements.

Specifically for 4th one Seirei no Moribito and Juuni Kokuki come to mind, and probably Hyouka to some extend.

Gosick - 1,2,4,5

Code Geass. It is a mecha anime, but it is a MASTERPIECE. It has mind games, and a VERY smart Protagonist with a "special power", who is at times evil.
The fights are also NOT for the sake of fighting, but instead to show if the strategies of the main character work, or not. Character developement is also good, but the power of the Protagonist is influencing that part also (I don't want to Spoiler it).

So all criteria 1,2,3,4,5 apply here.

It is splitt in 2 seasons:

Code Geass
Code Geass R2

Why I did forget to mention Code Geass in my post? :eyespin:, Seconded for sure.

Code Geass, main chara is similar to L.

Fate/Zero - Emiya is an anti hero. There are a lot of characters with twisted personalities. Series are action based but fights don't happen out of blue. There is a lot of tactic involvement, mind games. Talking, character developments. And great graphics. Worth a watch.

GTO fits under point 4. It is a unique comedy where a lot of character development happens through tout the series. Onizuka is a perv but he always manages to help his students in the most weird ways.

Mahou Shoujo Madoka★Magica is about mind gaming and manipulation. Main chara is a wimp though but there is Homura who plays big role and is like anti-hero for most part.

Mosnter is all about mind gaming. A doctor had saved a child once and that child turned into a serial killer that plays with peoples' minds. Doctor is determined to stop him.

Phantom: Requiem for the Phantom - main character gets brainwashed and is forced to become a serial killer. He is taught by the best one named Phantom. He starts weak but eventually becomes the best assassin out there.
Mind playing, settled action, character development, not a very positive main chara. Has almost everything you want.
Though series have 2 two time skips. I liked mostly 1st part but majority prefers 2nd.

Steins;Gate is about mind games too. The guy creates time machine and starts to make small changes to the past but results eventually become catastrophic and he is forced to get everything back to normal.

I would have to recommend Fate Zero. It fights all the criteria. There are plenty of fights but none of for the sake of it.

I recommend Spiral, though the MC is not evil, he is incredibly smart and his mind battles with several key characters in the anime is one of the main highlights of the show.

Wow, a lot of suggestions! Thanks!

I've already seen Fate/Zero, Code Geass and Gosick. I hear a lot about Evangelion, but there's something on it that displeases me. Oh well.

Monster specially is one that has been following me for a while now. Time to give it a try, I think. Phantom: Requiem for Phantom looks promising too.

Is Steins;Gate similar to Chaos:Head? I've read in an anime site (I'm not sure if I can post it here lol) that it's an "alternative setting", but idk what this means...

From what I've heard Stein;Gate is written by the same guy but the anime adaptation is leagues better (I've only seen Steins;Gate but it's a excellent anime all the same)

Steins;Gate >>>>>>>>>>>>>>>>>>>>>>>>> Chaos;head.

Steins;Gate is a no brainer if you like Death Note. Personally though Death Note sucked after the first half. Steins;Gate does not suffer the same fate.

It fills all your requisites except for #2. The main char is super good and SO COOOOL (you'll get the joke).