Anime characters are mean't to look American. Anime should really thank the Atomic bombs for its creation. After WWII people in Japan had nothing to do and needed entertainment. Eventually japanese cartoonists started producing their version of American comics (Manga ring a bell?). When they produced those comics, they also copied off the American's drawing style, and they added on to it (ie big eyes, crazy hair). From Manga came Anime, and in Anime came that same style of drawing characters.
Thats a very brief summary of why Anime characters don't look Japanese. Some don't even look like they have a nationality though, due to the different styles of different artists.