Oh, yeah. I have been talking a lot about anime lately. But have been working hard in my studies as well. Anyway, it's a pain in my heart to choose only 5 animes. There are a lot of masterpieces and I have not watched all animations (it's impossible). For a matter of taste, I just say that this compilation is not fair (for you, maybe), and my criteria to choose the order is very simple: psychological impact. By the way, I just like of any kind/genre of japanese animations. However, I don't like all animes. Let's start...
#5 - (Mushishi)
A masterpiece. The history, the soundtrack, the characters... perfect.
#4 - (HAIBANERENMEI)
This animation has a special place in my heart and mind. What a misterious and moving history!
#3 -- SERIAL EXPERIMENTS LAIN
Lain was my favorite character for a long time. This anime is so mindfuck that I had to watch it three times.
Because I already posted the opening, now I will not.
#2 - (GHOST IN THE SHELL SERIES)
Like Lain, this is the animation with the best approach and development of the cyberpunk theme. Also, a very mature history, with intriguing dialogues and action scenes. More than perfect.
#1 - (AKU NO HANA)
Oh, This face of Nakamura staring is so disturbing. I can't help myself but like her.
EDIT: I'm finishing read the manga. I HIGHLY recommend you do so, if you liked the animation. It's so, so amazing. Incredible. Actually, I realize why manga usually is superior to animations.
That's it. Of course, I would wish to put more animes on this list, such as Evangelion, Ergo Proxy, Fate Stay Night/Zero, Dantalian no Shoka, Madoka, among others. But, this is my taste. I also enjoy ecchi, harem, mahou shoujo, shounen, and had saw beautiful movies such as Hotaru no Haka, Street Fighter... Enough!