The anime storytelling style is often very different to that of western visual media. Many of the differences focus on a more gradual build up of the universe in which the story is being told, and more time spent developing the characters.
Many of these differences are shared with, and to some extent derive from, manga which Scott McCloud briefly touched on in one chapter of Understanding Comics.
One of the creative teams I adore is Clamp but, alas, my first example must be the second series of Magic Knights Rayearth. Frankly the story in the second series needed to be told, and it would have made a great 13 part series. Unfortunately it was 20 episodes which rather detracted from its impact.
Similar comments have been made to me about the Kimagure Orange Road TV Series, although as I recall the suggestion was that the 40 episodes could have been sweated down to about 13 without losing much (if anything). [Aside: I haven't seen or reviewed the TV series but my review of the OAVs and 1st movie is available here.]
This syndrome is particularly evident in martial arts anime, particularly when they degenerate into "opponent of the week". Or in some extreme cases half of that (Flame of Recca, Rurouni Kenshin, and Bleach all suffer from this in various parts of their story arcs).
But, as always, there are exceptions. Series where tight disciplined editing vastly improves the storyline. I'm sure that readers will chip in with examples for debate (hint, hint) but to get things rolling I'm going to only name one. The Vision of Escaflowne was initially scheduled to be a 39 episode series but budget cuts forced its reduction to 26.
What the production team didn't do was abandon any of the story elements; they just edited the pacing of those elements to fit them into the 26-episode format. The result is a series paced like a roller coaster that never lets up and only gets faster as it goes along. And it works, oh boy does it work.
For this and many other reasons (some of which I may discuss in a formal review one of these days), Escaflowne is one of my all time favourite series. The pacing is flawless and creates an almost addictive desire to watch the next episode as soon as you can. After all, they're only 22 minutes long, one more won't hurt...
At 39 episodes Escaflowne would have been good, probably even excellent. At 26 it is a masterpiece and a true classic.
Moral of the story: Sometimes less is more. Learn to edit dammit!