The following post is my response to The Mask's challenge to make a list of what you think (objectively and/or subjectively) were the best anime of the last decade. The list is in no real order, since that would take far too much pondering and internal debate for me to figure out. Please enjoy~
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#1 - .hack//SIGN
It only seems fair that I should have some .hack up on here. After all, .hack//SIGN is what really started it all for me. The anime itself boasts some pretty animation and amazing music, and let's not forget the mystery that is the story. Some people knock SIGN for being boring and far too slow, but I like the subtle character interactions. It lets each character show who they are without having to directly state so all the time.
#2 - Eureka 7
Another series that shows off some great characters, Eureka 7 isn't just a mecha show. It's simply a great anime. It feels like E7 made very good use of its time (50 episodes). The whole thing is very much about relationships between people, especially love. Renton and Eureka have some very cute and touching moments, and hey if you get sick of the main pair there's always my personal favorite Dominic x Anemone.
#3 - Moribito
Man, talk about gorgeous anime! This one probably has the best animation out of the whole list; it's just damn pretty to look at. But more than that, the characters are refreshing. You have Balsa, who's a strong woman and can fight for herself, but she never falls into the cliches that you think she would. She's just a fighter, who's not dressed like a slut (which is the real breath of fresh air here). The story itself is fun too, but again I just liked learning more about the characters as the series progressed.
#4 - Planetes
I love this show. I really do. I think it gets overlooked for far flashier anime most of the time, which is really a shame. It's the best portrayal I've ever seen of futuristic space exploration. Mankind has not been able to explore the entire universe yet, nor have they settled colonies on Mars or anything like that (well, except the Moon). There is better technology though, and with this comes more problems, which is where our main cast comes in. Really, it just has a great setting and yet again I love the characters and their development.
#5 - Code Geass
At the other end of the spectrum we have Code Geass. Directed by Goro Taniguchi, the same man who directed Planetes in fact, this show is crazy. The animation style is funky (and fanservice-laden), the plot is zany, the very facial reactions are insane... but it's all so much fun. In all its wtfery, I had a blast. And honestly, how could I not mention the show that gave us ACTION HORSE?
#6 - Mushishi
Mushishi is another show that I'm picking largely for the characters, not that it has a very substantial main cast. The protagonist, and really the only guy who appears every episode, is named Ginko. Ginko is a mushi master, a person who deals with these strange, almost otherworldly creatures called "mushi". The show is very episodic, dealing with one case of mushi after another. In that way, we get to learn more about the people who are affected by it, although only in one episode. There's a large variety of personalities and tragedies though, so it never gets boring. Plus, you slowly get to learn more about Ginko as the series progresses.
#7 - Fullmetal Alchemist
This is one of the few really sickly popular series that I actually like. The first anime produced (which is the only one I'll be talking about here) is quite powerful emotionally. Stuff happens to these people. BAD stuff. It's not always easy for them either. Really, it was just a fun ride and I couldn't go without listing it on my top ten.
#8 - Samurai Champloo
Coming from the same creator as Cowboy Bebop, you can see a lot of similarities. Although the two series take place in very different settings, the pacing and direction are obviously similar. Samurai Champloo is episodic as well, even though there is a bigger goal that the main cast has in mind. This is simply a fun show to watch, plus Fuu is one of the best female protagonists ever.
#9 - Tokyo Godfathers
I love Satoshi Kon. I think he's a great director. Tokyo Godfathers is different from his other works, in a good way. It's centered around three homeless people in Japan who find an infant in the garbage. Again, it's one of those anime that nicely develops its characters as everything moves along. You slowly learn the past of "Ms." Hana, Miyuki and Gin as they take the baby, Chiyoko, back to her mother. Funnily enough, Tokyo Godfathers is something to watch around this time of year, considering it's set during the holidays.
#10 - Gurren Lagann
I gotta love this series for being so balls to the wall, "we can do it!" crazy. It's not the same kind of crazy as Code Geass, oh heavens no. It's more of a controlled crazy; basically it was directed very well. Even though the show has some obvious fanservice (*coughyokocough*), those characters are actually still interesting. Despite the breasticles, I still like their development. I guess the best way to summarize Gurren Lagann is simply to say, "It's epic."
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Honorable Mentions (since they deserve it):
Lovely Complex, Millennium Actress, The Twelve Kingdoms, FLCL, and plenty more I'm sure.