The saddest moment in anime history has to be during episode 21 of Chobits. It's the only anime I've cried over.
--spoiler
It's when Uedas persocom pushes him out of the way so he doesn't get hit by that big truck. The music is what really made it sad. I thought the persocom was going to stand there while Ueda jumped out of the way. But she pushed him out of the way! I cried :blush:
Another sad moment was when Sorata died during the X series.