A bully belittles those whom he/she perceives to be weaker (emotionally and / or physically). Often this is done in front of an audience of peers. The bully is hoping to improve his / her social standing through intimidation. When bystanders laugh or even remain silent, it encourages the bully to persist in the behavior. The victims are left humiliated and angry.
One of the most powerful ways to stop a bully is to coach the bystanders. When they stand up and confront the bully, saying things such as "you are definitely not cool" or "maybe you'll stop this sort of thing when you become mature" the bully learns that he/she is actually losing social standing through their behaviors. This is the opposite of what they're looking for. When they learn consistently that they lose ground socially when they bully, the behavior will stop.
A newer version of bullying, cyber-bullying is when something intimidating and belittling is sent to the victim, and the bystanders are copied in the e-correspondence. The same method of stopping the bullying applies. The bystanders need to let the bully know that they do not approve of the behavior.
Approaching the authorities (parents, teachers, etc.) has its place too, but nothing is more powerful than the bystanders becoming unified and letting the bully know that they are losing social standing from the behavior.