relic, I was inclined to write a response when I first read your post last night, something that would fulfill your request in terms of content. Unfortunately, after spending some 10+ minutes brainstorming, I realized - once again - I lacked the wide-spread knowledge to make a comparison such a yours, despite the fact that I have watched 150+ series/movies so far (according to my ratings file, which I am sure not much) and that I would end up with a post complementing yours, nodding here and there at most. The problem is, I watch anime for entertainment only, I would probably have trouble comparing Kanon to Clannad

Never-the-less I would like to give it a try, because apparently some of my favorites are not given appropriate attention!! Unfortunately I can only come up with something that is highly disputable.
Ergo Proxy It should have attracted much more attention, genious piece of work, imo. Manglobe simply created a rocking female and a dumbass male character, embedded them in a post apocalyptic adventure to seek the truth, a little brainstorming for the viewer here and there, put a little comedy and drama inside and there you go.
You will probably say, "so there is nothing special about this anime series", but hear this - now this is all my speculation - in my opinion, the creators didn't give a rats ass to what the audience/publishers would think about their story line and they did not deviate from it because of fear of popularity or ratings as a result, they ended up with one of the marvels of this decade. One of those series that you should complete in a short amount time (a week may be) to maintain a grasp of fast moving events. Definitely needs a sequel in the next decade
Texhnolyze Yet another post-apocalyptic masterpiece. The first episode alone will help you realize how things are serious with this one. Unfortunately, it would be difficult to describe the plot without giving spoilers but let's just say the struggle to survive is at the center of the plot of Texhnolyze and I assure you, it will be one hell of a struggle and this time there are no heros to save the world.
The main characters in the story are so serious and dedicated to their individual cause, you might start to think they are not fictional at all

The pace is slow at the beginning and tries you from time to time but being patient definitely pays off. You will realize how dangerous we humans are, in a fantastic way
Twelve Kingdoms Yet another marvel of this decade, despite the fact that it can bore you death at times. Simply put, I can’t stand crying/whining people, especially girls (in TV only).
Never-the-less ONO Fuyumi, the author of the novel that series is based on, definitely has something in mind in terms of character development and she is quite good at it which might have been my sole reason to finish this anime.
Apparently when anime creators adopt a novel instead of a manga, they can often come up with better results, imo. That is probably because the novel author gives importance to detail in the story which unfortunately can not be achieved with a manga and that detail is very important in terms of character development and visualization of the story.
Clannad & ~AS~I am telling you, the authors of this series decided to torture us with this one. It was all fine and dandy until episode 16 of Clannad ~AS~. In that particular episode, I was in tears and couldn’t continue the series for 2-3 days (seriously, you get more emotional as you get older)
Kanon had a similar impact but not at this magnitude. I refrained myself from watching Air.
GTO Seriously, I am unable to compare GTO with anything I have seen. This is not one of those series that has an incredible plot, definitely can not be compared to the ones I mentioned above, but in the end it makes you laugh.
Just imagine what happens when you mix an ex-gang-leader and a school teacher, you end up with Great Teacher Onizuka. He is definitely fun at times and one of my favorites for this decade.
[note] I will try to continue with new additions to the list, I will edit this one