Not many Americans realize that early Japanese animation was HEAVILY influenced by early American animation. In fact, the reason that anime characters have big eyes is because American animators depicted characters with big eyes. Japan was largely isolationist until the late 1800's and early 1900's. When Japan opened its borders to Westerners, it adopted and improved 200 years worth of Western technology in 50 years. Animated cartoons were part of this technology.
Here is an example of 1930's Japanese animation:
Here is an example of 1930's American animation:
They are actually very similarly drawn aren't they? Actually, Disney was probably the greatest foreign influence on early anime. Ancient Japanese art and history mixed with American technology and style to give anime a style all its own since the 1930's. Here is a short video showing how anime style has changed over the years:
Now, it seems that anime is coming back and is now influencing American animation.