I've been to Japan, and I didn't want to be treated like a
little prince, I wanted to be treated like everyone else. Not better and not worse.
But it wasn't like that. People always tried to speak to me in English even when I demonstrated I could speak in Japanese. I saw onsen with "no foreigners" sings in front. Because my "race" can't be easily identified, I was more often than not asked where I am from, where my mother is from and where my father is from. I've heard of incidents where people of Arab-looking descent are stopped and questioned by police officers.
Are these examples of racism? Probably not (at least from my experience and perspective), however they are in my view, examples of a deep "us and them" attitude which ignores the fact that culture can be learned. Maybe it's naive of these people (or me), or there is some xenophobia etc.
I think perhaps the most convincing thing for me (not an example of racism) is where we have the situation of someone who has taken up a "Japanese" life in that he has become a citizen, has lived in Japan for an extended period of time and interacts daily within society. Most Japanese would not consider this person Japanese - but what more could such a person do to be Japanese?
This identity issue is provided from the outside, for inside he can feel as Japanese as he wants and get nowhere. On the other hand, if we were to put the situation with the US or perhaps a Western European country, we would see that a person would probably be more readily accepted as an American or a Brit.
Does racism exist? Probably, but it's certainly not as plain and commonplace as little hints of xenophobia and anything foreign being perceived as not-belonging or a little novelty.
Here's an interesting document worth reading: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1551462
It's called "The Wajin’s Whiteness: Law and Race Privilege".