So, I've seen a few interesting lists with some titles that I might want to check out based on the descriptions.
Here's my current list, although I'm sure it will change quite a bit over time, since there is so much I haven't seen yet. As for the rankings, I'm confused about #2, since I just finished it- not sure where in the top 3 it should belong, and the last two I just sorta threw in there (I was considering stuff like Hunter X Hunter, Rave Master, Yuyu Hakusho, and Kino's Journey, to name a few).
1. Elfen Lied
What drew me into to this show was the intensity mixed with the extreme violence over the beautifully crafted storyline (as unlikely as it may be). The deaths are gruesome, but it's not like a standard horror scenario where you just don't care. They make every effort to express the death and violence to be as traumatic as possible (I'd say the whole tone of the show is "expressionistic"). Amazingly, I wouldn't even say the characters are the most likeable (not to mention there is too much fan service), but it somehow hits the spot.
2. Higurashi No Naku Koro Ni
I've just finished watching this show and I'm honestly not sure where to put it. It could very well go as #1 or #3... I'm leaning toward calling it my favorite, but it could be just because I still can't stop thinking about this amazing show. Anyways, what I like about this show is first of all, the fact that it is confusing. Very confusing. This will turn people off, probably, but if you just chill out and accept the confusion as an inevitable part of the viewing experience, you might just learn to enjoy it. There are so many details and so many ways that the characters can develop (though mainly the different stories illustrate each character's descent into insanity). I don't view this show as much of a horror anime, but as an experimental mystery tale that has incredible scenarios, atmosphere, and moments of both deeply contemplative dialogue and excessively intense brutality. In a way, it combines some of the best aspects of my other favorites- such as the intellectual focus needed to understand what is going on that you find in Death Note and the Expressionism found in Elfen Lied.
3. Gantz
(first of all, the manga is much better, and the ending of this anime should have never existed)
I'll admit I like the gore in this show, too... hehe. But, as with the other two, it's more than that. This I would also call "Expressionistic" (they tend to be my favorite, can you tell?). The whole scenario in this show is out of this world, completely bizarre and fascinating. I think that little onion guy offering everyone "do you want a spring onion?" made me laugh a bit. The overall character development is some of the best I've seen in an anime, and their interaction and companionship grow, and it becomes all the more tragic when the main characters die right in their faces. Possibly my favorite scene is when Kurono gets back from an especially horrible mission, and he is the only one surviving. After all that, he only gets 10 points... (and he gets so mad he starts shooting the Gantz ball even though he knew it would do nothing). That type of playful mockery (especially the whole Good Morning song played before every mission) on top of such tragedy is so unique and spine-chilling, and I've yet to encounter anything with an effect quite like it.
4. Death Note
This is more of an intellectual series, and I'm surprised it's so popular. It just keeps you hooked, and guessing at all of the possibilities given the unique scenario of owning a Death Note and trying to avoid getting caught. It also raised philosophical questions about power (though fundamentally a question of vigilantism). It's actually pretty fascinating the amount of thought that the author must've put in to make this whole story work out the way it did. In the end, though, I'd have to say, given who I sided with, the content of what happened just sucked but the overall dramatic impact was probably one of the greatest in any ending of any show, ever. And that's the important part.
5. Welcome to the NHK
Very, very depressing and philosophical series. Makes me want to read Schoepenhauer after watching it, lol. I think this show reveals some very disturbing truths about life... probably the only thing holding it back from me liking it more is that it's more of a real-life situation, and nothing supernatural occurs- just some hallucinations from time to time. Also, the fact that much of the story revolves around the main character in his messy apartment gives it kind of a claustrophic feel to it- it's great, when, for example, he goes out and talks with the girl in the park at night.
6. The Melancholy of Haruhi Suzumiya
I don't know what I like about this show so much to have it as #6, or maybe I've forgotten why I like it so much, but it's there. I know I don't care for the experimental ordering of the episodes. Maybe it's just that the characters are likeable and that it has Mahler and Shostakovich as part of the soundtrack? Either way, it's just a very enjoyable show that can be hilarious at times, and for some reason I like the constant rambling of Kyon, as the narrator... (who knows why)
7. Full Metal Panic! (includes all seasons, my favorite being Fumoffu)
Although the action in this series is great, what I like most about this show are the sections where Sousuke is at school with Chidori. There seems to be an endless variety of wild, imaginative and hilarious scenarios that make this the most charming anime I've seen.
8. Now and Then, Here and There
This probably deserves to be ranked at 5 or 6, but this is just my taste. Now this is an endlessly bleak series from beginning to end (the ending is a happy one, but it's hard to help but feel miserable still). Take the most screwed up world you can think of and place f***ing Ash Ketchum in it. The protagonist's optimism is quite the spectacle, especially during scenes such as the one where he doesn't let the girl abort her own baby or drown herself. He eventually makes things turn around, always saying that there is something good enough in life that'll happen eventually that'll make it worth it.... oh yeah, and King Hamdo. Wow, what a character. That is true madness. I think my favorite line was after he conquered every single village in the world, and effectively became ruler of the world- he looks out into the desert and slowly gets agitated. Then he bursts out, "Abelia! Do you realize there are people, hiding in the sand, who dare defy me! I can't take it" or something like that. The sad part is, the kids who are enslaved in the system who realize that they have no home to return to eventually become corrupt with delusions of power, not dissimilar to King Hamdo. A really sad cycle.
9. Chobits
Charming, quirky, funny... passionate ending. I don't know what else to say, it's been a long time since I've watched this show.
10. Serial Experiments Lain
I like experimental stuff. I probably won't ever completely understand this show, but that's the fun of it. The presentation is very interesting, too, especially how every episode starts off with shots from the traffic in the city. I don't love it, but I like it and admire it a lot.