For anyone in any field of animation - 2-D, 3-D, stop-motion - respectably, it is very understandable that anime can be seen as an infamous form of animation. The flat and static movements, the inconsistent dimensions of the characters when they rotate, the notorious habit of using only two key frames for the mouth when someone is talking (what bugs me is that often times, the jaw or chin doesn't move with the mouth or lips...grrrr). And there are many overly-popularized shows that emulate these annoyances.
However, having been an anime fan a great deal of my life (and in some cases, still to this day), I know that there are still great animators and films to be seen, even in Japan. Of course many may already assume the greats like Hayao Miyazaki or the film "Akira" - and frankly, who wouldn't? But I guess to just be a snob, I wish to present a list of Japanese animated films that in my mind, not only have extraordinary animation, but great and twisted stories and vibrant characters.
Tokyo Godfathers (I'd say see this one FIRST! An absolute classic!)
The Millenium Actress
The Girl Who Leapt Through Time
Jin-Roh: The Wolf Brigade
I wish I had more, but just in case, some really good animators and studios to look into are:
Any one of these films or animators will at least be a good bastion of animation to kind of even out the criticisms against anime.
Out of all the crap in anime, at least these are a sanctuary from all of it.