Perfect-blue (generally I like my anime with plenty of robots, demons, swords, etc... and perfect-blue has none of these, it is what is known as a suspence thriller, but the animation is superb, the plot is facinating, and the characters are endearing. I don't think it is the 'best' per-say, but it is one that everyone should see.
Another that everyone should see is the series 'Patlabor; mobile-police'. There are in-fact Patlabor movies too (two of them that I am aware of) but I would recomend one see at least a few episodes first. Patlabor has plenty of big robots, great story-lines that are sometimes serious & intense and other times light-hearted & funny, it also has some of the best characters in Anime. My only critisizm is the animation which is not bad but inconsistant.