As I understood the OP, LibraryLady was asking for possible solutions to mitigate the problem of bullying, which exists worldwide from what I can tell. Thus far, the only reasonable solution I have seen proposed in this thread is "education", although the type is not specified, and requiring the teachers/caregivers to own up to their responsibilities in caring for the children that are under their care for the period that they are in school. I agree with both of these, and would like to take this a step farther, if I may.
I'm not about to get into the whole discussion regarding what bullying is and how the victims should respond; I managed to get through school despite being bullied due to being more intellectual than the others around me (I wasn't the smartest person in my high school class, but I wasn't far from it) largely because I learned to not care what others thought about me, but that took time and a lot of therapy to accomplish, and I fully admit that I still have some issues stemming from that time in my life. However, I have given the problem some thought and would like to present my perspective on it. Given that I am from the US, my comments will apply largely to that culture, but the solutions I'd like to propose could very well apply worldwide.
Basically, I see the main problem as being a sense of entitlement. Children of this generation (I'll call them Millenials; picked up that term yesterday at an off-site with my company) grew up in an age of technology, when having the latest gadget was not only possible but often easy, depending upon your socioeconomic background, of course. Most teenagers these days quite frankly piss me off, because of this sense I get from them that they expect everything to be handed to them without their having to work for it, and they therefore look down on those who don't have what they have. They make fun of the poorer people, and don't have to work for their educations the way people in my generation did, because we didn't have smartphones that could look up the answer in the blink of an eye with very little effort. I see shows like "My Super Sweet 16" on MTV and the selfishness of those little punks just infuriates me. I realize that is a very small subset of the teenage culture, but when I see a sixteen year old young adult throwing an absolute tantrum because they weren't given exactly the right kind of car on their birthday it utterly pisses me off. My parents gave me a car on my 16th birthday, yes, along with a credit card and helped me set up a checking account, but the car in question was used, and I was responsible for getting the money to pay for gas, car repairs, and to pay the credit card bills. The end result of that? I am fiscally responsible, paying only for those things I know beyond the shadow of a doubt I can afford, and I have very little debt to my name. The likelihood that any of today's Millenials would be in my situation when they're my age is, as far as I am aware, pretty damn miniscule, and all because of that sense of entitlement and selfishness I spoke about before.
So, education. What kind? Well as I see it, it's going to have to be delivered in several different ways. First and foremost; parents need to be held responsible for their children's behavior, which might spark a movement of actually training their kids for the real world as opposed to the world that exists only in the confines of school. One suggestion for that would be to require parents to attend some sort of family counseling after the second strike for the child for a mandatory period, although I'm not sure that's legally possible; however I am providing what I view as a potential ideal solution here, not what is necessarily likely to happen. I'm of the opinion that if parents are made aware of what their indulgent attitudes toward their precious darlings will do to said darlings, they might actually wake up and start being legitimate caregivers, although I'm perhaps hoping for too much in some cases; regardless, it remains a suggestion.
Secondly, schools should disallow the use of any kind of technology excepting what is absolutely necessary to carry out the basic functions of the class in question. In other words, cell phones, PDAs, cameras; everything should either be locked in an individual locker upon entering school buildings or should be left at home or in the car, assuming said student is capable of driving. Any student caught violating this rule should be put on probation and punished appropriately. Exceptions could be made for certain functions, such as if the class is photography or is doing some sort of special function that a student wants to photograph or otherwise record, but otherwise the student should only be allowed pens/pencils, paper, a basic (or graph, in the case of advanced mathematics classes) calculator, and their books. I didn't need much more than that in order to pass my classes, so why they should be allowed to bring their cell phones or whatever to class is utterly beyond me; it potentially promotes cheating if the teacher is not hypervigilant, and contributes nothing to a student's education. This is a possible solution because, if no student has their little bits of technology with them at school, they have less to hold over students who may not possess the latest gadget. What's the point of bragging about your gadgets if you don't have them to show them off? And what's the point of needling someone if you can't flaunt your good fortune in their face?
Thirdly, and I feel perhaps most importantly, students from about age 10 on up need to be educated about what they will face in the real world. There should be life classes given to the students starting at about age 10 where they are presented real world scenarios and asked to study how people can react to them. For example; if students are shown the example of someone who loses everything they owned due to mismanagement or some other means, they might realize that their individual circumstances can change in an instant if they aren't careful. Beginning at age 14 and leading up to graduation from high school, I believe students should be required to spend at least two years, five hours a week, involved in some sort of volunteer service program that is outside of school. This can include volunteering at soup kitchens, joining Greenpeace or the Peace Corps, volunteering at hospitals, homeless shelters, shadowing somone in a position of service, and actually being confronted with what it's like in the real world. This can be for school credit, and lets face it, that sort of thing looks GREAT on college applications. It forces the student to confront the fact that just because they're the **** in school, in the real world, they're just another person starting from the bottom and working their way up.
Lastly, as others have suggested, holding the students that are bullying responsible for their actions is key and paramount to mitigating their behavior. This is going to require change on the part of teachers and administrators moreso than the students themselves, but if there are negative consequences for behavior, generally speaking people learn not to repeat said behavior.
It may not be the only motivation for why bullies act the way they do; I'm sure a good part of it is that we are psychologically inclined to pick at those who are different from us, but I'm of the opinion that applying some or all of the above solutions might mitigate to a great extent the bullying issue. I offer up my solutions to the thread; please feel free to discuss, question, pick apart, whatever you wish. I just wanted to offer some more detailed possibilities for correcting the behavior than have thus far been offered, IMO.