It's very easy to find people who are kind and will accept you in Japan. If you don't look Japanese, you will get some stares, but it's relatively harmless. If you are staying with a host family, they don't care. They are mostly pretty stoked to have you come live with them!
Going to Japan is a really great experience, so don't get weighed down by fear of discrimination!! Keep your head held high and be proud of who you are!

Unless someone is going into the deep country, "stares" is something that foreigners really don't get anymore in Japan.

That's what I thought, but I when I went this summer I got quite a few odd looks on the trains...

It may not have been because you are a foreigner. It could have been because of any number of reasons. Generally anyone over the age of 6 doesn't find the need to stare at foreigners.

Possibly, but I had many friends who went at the same time I did have this problem.
Also, I understand that a few people staring on trains does not reflect an entire culture (I fear someone will jump in with that remark soon >>), and that it had absolutely no effect on my time in Japan. It was simply interesting.
Japan itself was a lovely experience, and I plan on spending a year there in college.

Sometimes people stare out of curiosity, so just smile back at them. The smile will probably be returned and the staring stopped. If its the rare instance where the stare includes disapproval, you would accomplish the same thing. They would probably ignore you after you acknowledge them politely.

That may be more because you seem approachable than because you look like a fellow countryman. I am as Anglo as they come, but on my last trip to Mexico City I was frequently asked to assist total strangers as if I was a native, even by Hispanic women. I had one New Yorker come up and try speaking to me in Spanish! Once I answered her in English and gave her the directions she needed, I asked why she came up and asked me in Spanish from her pocket dictionary. She said it was because I looked quite comfortable in my surroundings (not like a tourist) and friendly. So even though Asian tourist in Hawaii may have picked up on a subtle visual clue to your heritage, its even more likely that they thought the same about you as the lady did about me...... a native and friendly.

What would happen if I picked up some dirt and threw it in their face. Then, whilst waiting for a reply, I started throwing rubbish from a nearby trash can at them??? What would happen? I've always wanted to try this.

You would be acting like an antisocial dolt, which is frowned upon in all parts of the world.

I was in Japan in 2008. I got stares. Sometimes I looked at the person and smiled. Mostly they turned away when I did this. Some smiled back and a couple came over and talked to me. I was making a confused look at a train station and a guy who was like 6 feet 4 inches was staring at me. When I looked back at him he came over and asked me in English if I needed any help. Japan was awesome!

So I'd get frowned at? That's all?