Plot: 8.5/10 -- Rich in detail and very complex. The idea of different universes existing for every choice, with the you in that universe going down a different path, is truly fascinating.
I have to mark it down a little because of the slow pacing and unexplained elements of the story. However, I'm sure someone who has a better understanding of quantum physics would add 0.5 to this rating.
Characters: 9.7/10 -- Watching the main characters develop in Noein is different than in any other anime I've watched. You see how they *possibly* look and act in the future throughout the show (sometimes even more than one possible future version), which creates thoughts and shows the characters from different angles.
My favourite characters were not the main two (Haruka and Yuu), my favourites instead being Ai and Isami. It's both funny and cute seeing them try to hide their feelings for each other as the series progresses, Ai being a fiery red/orange-head and Isami being your average male - Unable to pick-up on signals. Isami's character is probably my favourite due to the future versions of him shown.
The only real bad character point I can think of is Yuu's character - He gets quite annoying with his attitude. The annoyance is worsened by slow plot progression.
Art: 9.5/10, Animation: 9.5/10 -- I can't rate art and animation accurately since I know nothing about it.
Noein looked amazing and fairly unique to me from the moment I first saw it. The start of the show showed that it obviously had quite a big budget, combining CG with excellent art and animation. The show kept up the high quality visuals until the end, although the less important episodes didn't get the attention the more important ones did.
Sound: 9/10 -- I'm probably being quite harsh here - The soundtrack is outstanding. The the choral battle/action music really gets you excited, the dramatic music does its job, the cute/funny music is fun to listen to... It's all great. My only reason for not rating higher is because there aren't too many tracks I'd want to listen to when not watching the series.
Total: 9.2/10 -- All in all, an amazing series. This is a series every anime fan should watch.