Have you encountered discrimination or prejudices in Japan ?

[Glenski]

In the States, I have learned that what the police are allowed to do, what they say they can do, and what they do do are three very different things. Considering what I've heard about Japan, I'd be surprised that the cops there are all that different.

That doesn't make it right in any country that recognizes the rights of human beings. But we're getting slightly off the track here.

I had a Korean student that told me that it is because they stare at the unusual and different. Therefore, they stare at foreigners, and she explained it as curiosity. She even got into trouble staring at people on buses and trains in the United States, and wasn't sure why. I told her that it is considered rude here and to stop doing it, period. I explained how it makes people uncomfortable and sends the clear message of, "You are different, you don't belong" to people. I think she was being pretty honest about not meaning anything by staring, especially because she told me that she thinks Americans are the most misunderstood people in the world (but that's a different conversation). But it was a bit of a shock to her to realize what she was doing in our mindset.
Then again, she was Korean, so maybe Korean motivation for staring is different.

Actually, I don't think the motivation is any different for the Japanese.

Besides, I hear that people stare on the train at each other in Europe all the time.

Hmm, interesting. Been there twice now (England, Scotland, Belgium) and never saw that happen. But what you are describing here in general terms can be explained by the fact that European countries are used to people traveling within their borders from other countries, and people don't look all that differently because of proximity or intermingling of races. It's different with the "homogeneous" Asian cultures. We non-Asians stick out.

it is unlikely that any Japanese person would be so overt [as to stare].

I totally disagree!

I usually follow it up with a description of how I've had friends refused cab rides or restaraunt service in their countries because they were foreign, with an explanation of what real racism and discrimination is (firehoses, lynchings, Jim Crow, etc).

Those are just more overt (to use your word) and more violent manifestations of racism and discrimination. One can be discriminated against without violence, don't you think?