This article in the NYT is superb. It's only a three-minute read, but makes some exceptionally important points...
[some] children bully because they have emotional and developmental problems, or because they come from abusive families. They require our help more than our punishment.
Another great quote,
Children need to know that adults consider kindness and collaboration to be every bit as important as algebra and reading.
The key point, for me, is that if we want our children to stop bullying, we must not attempt to dissuade them from it by being "bullies" ourselves. That is, punishing them, giving them detentions, involving parents and getting them into trouble, and all the other punitive approaches that are so common simply do not work.
Creating a sense of community, kindness, responsibility, and involvement make far more effective outcomes. Of course, this is not as easy as the band-aid solutions that we see through promised rewards or threatened punishments.