The Hows and Whys of My Tastes

Title totally not a spoof of Naze Nani Nadeshiko. In any case, here you go some 3x3s as a start.

Haruhi

Great subtle scifi with great characters and lots of plot continuity. Read the novels, in any case, only after them I decided that this franchise has a well-deserved place in my top list.
Best characteristic is how it works on several different levels.
First you have the cream of the coffee, the story about a teenager Mary Sue who has lolcrazieh adventures, and her compatriots of the always-happy Koizumi, the cute bookworm Nagato and the sexy maid Mikuru, whom just so happen to not be normal teenagers either; all of this provided with the commentary of the self-insert male character.
Then you have the face value scifi about aliens, time travelers, espers and gods.
One level deeper you have the fictional work consisting mainly of character analysis.
Another level deeper, and suddenly the long-winded conversations with Koizumi become the main point, so that in your hands you have a discussional work on common ideas for TE, scifi worldbuilding,  the human psyche and so on.
I can probably continue this, for example mentioning the phrase "Unreliable Narrator", but it'd start to sound stupid even in my own ears, so let's leave it here. Just one more thing: any of these levels can work by themselves. You are not required to see this series from all these viewpoints too to be able to enjoy it. That's pretty neat.

*monogatari

Damn you, nishioishin! I did not sign up for having one fictional work to present and agree with 50% of the non-trivial ideas underlying my sense of morality. And THEN to present handfuls more of the morality shades you usually don't see in any work - either because they are not mainstream enough for the normal populace, or because they are not loldeep enough for the "connoisseurs".
The facts that I constantly drool for Kanbaru, am a total fetishist for the stereotype of Shinobu, and think that Mayoi is a total bro and the best character, are just supplementary. Seriously. My opinion is totally not based on my desire to fuck Karen senseless.
Not so irrelevant is the fact that the Shaft adaptation made everything at least twice better. Except that I still miss some of the omitted conversations, but oh well.

Diebuster

This is it.This is how it should be done. This is how every second should not be a waste. This is how every detail should fit. This is what I love about designs, and animation of the simple gestures, and colors, and the way the voice breaks a little, and the choice of words, and the little things from one character which another takes and embraces, probably not even realizing he did so, and [...]. This is the true power of making a parallel structure. This is far from just an optimal technical execution and great directoring. This is not simply the writing and The Story, either. This is not complete with just the ideas, invested and interwoven inside. This is what I love about scifi, no, fiction, no, to say it decisively, human art as a whole. This is what I emotionally invest in. This is where my role models can be found. This is me.

Sketchbook ~full color's~

The series which actually showed me what a wonderful medium animation can be. The highest point of slice of life... and iyashi-kei. It's pointless to discuss anything about its characters or plot, because what it does well is the atmosphere; and doing the atmosphere well is the strength of anime as a whole. If you want a plot, go read a book.

TBC:

Sayonara Zetsubou Sensei
Pani Poni Dash
Hidamari Sketch
Symphogeah
the works of Yoshiura Yasuhiro
Dirty Pair
D.N.Angel
Ben-to
Mouretsu Pirates
Fireball
Denpa Teki na Kanojo
Dantalian no Shoka
Black Lagoon
Kyouran Kazoku Nikki
Natsu no Arashi
Soredemo Machi ha Mawatteiru
maybe hyperlink to Katanagatari

Manga:
the works of Dowman Sayman
the works of Koji Kumeta
the works of Ueshiba Riichi
the works of Mizukami Satoshi
Getenrou
Tonari no Seki-kun
good fantasy (Negima, MaoYuu) <<that should probably be a blog post by itself
Chihiro and why she is best girl ever <<maybe this one too