Tenchi Muyo (and Universe - not Tokyo)
Princess Mononoke (and Miyazaki films in general)
Akira
Cowboy Bebop
Ghost in the Shell
I also think we need to separate this into 3 categories: Most Popular, Personal Favorite, and Best Overall. I realize that there's significant overlap, but let me explain:
On the subject of favorites: I love Dominion Tank Police to death, but I can look at it rationally and say, "That does not deserve to be on the short list of best anime ever created."
On the subject of popularity: Let me use as examples the two most popular anime of all time, DBZ and Sailor Moon.
DBZ: I did watch this show, but it had two major drawbacks besides the ridiculous power levels and inflation rate of same.
1. One could literally watch every third episode and not miss a thing. They start off by telling you in detail -- with clips -- the events of the previous episode, then do the episode, then tell you in detail -- with clips -- the events of the next episode. At least in the Toonami version.
2. The story usually took many episodes to move forward at all. I vividly remember that the two deadly androids 17 and 18, who were a planetary menace, spent at least a dozen episodes roaming the countryside in a pink truck. I think it was an ice cream truck.
Sailor Moon: Most episodes followed a formula revolving around the Monster-of-this-Episode, which often had at least one of the Senshi (in civilian form) -- or a love interest -- in dire straits, before the others saved the day. The transformation sequences were also ridiculously long, at least in the dubbed versions I saw.
Now, none of this makes them BAD anime -- on the contrary, there is a reason for their popularity, and it's not camp value. But it does, IMO, keep them off any kind of short list for "Best anime ever".
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So, to recap:
Best Overall:
Tenchi Muyo (and Universe - not Tokyo)
Princess Mononoke (and Miyazaki films in general)
Akira
Cowboy Bebop
Ghost in the Shell
Personal Favorites not included above:
Dominion Tank Police
Birdy the Mighty
Most Popular not included above:
DBZ
Sailor Moon
Ranma 1/2
Slayers
Evangelion
[edit: GitS beat out Evangelion for Best; dropped Naruto and YuYu Hakusho for Evangelion and Slayers in Most Popular.]
Tag (courtesy of fkusumot): "Please feel free -- nay, I encourage you -- to offer rebuttal."
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My advice to fanboys: Brag about stuff that's true, not about stuff that's false. Predict stuff that's likely, not stuff that's unlikely. You will be happier, and we will be happier.
"Everyone is entitled to his own opinion, but not his own facts." - Sen. Pat Moynihan
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The old smileys: 
; - ) : - ) : - ( : - P : - D : - # ( c ) ( k ) ( y ) If anyone knows the shortcut for 
, let me know!
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I have the most epic death scene ever in VGChartz Mafia. Thanks WordsofWisdom!
