Personally, I think this is a pretty sticky topic. On the one hand, I'm from the time where if you were being bullied and picked on, you either stood up for yourself and hoped for the best, or you just dealt with it until you could get away from it.
I was bullied in high school. Rough times, I remember, but I finally got sick enough of it to talk back. I stopped caring what that moron said and it eventually dwindled down to nothing. However, what worked in my case may not work in another's. There's also the notion that the world has changed a lot since I was in school. There's a level of technological saturation that can make it hard to get away from taunts and other crap bullies may pull. How many stories have we seen so far that have mentioned being bullied on Facebook or other social sites?
Now, I know a few people will think on that and respond with, "well, they can block whoever's being a jerk", or "it's only words on a screen; these kids need to suck it up", or something of the sort and to an extent I agree that kids should try and realize that. But that can be hard to do when you're of an age where what your peers think of you shapes you and provides some kind of reflection to you. Then, there's also the idea of helicopter parents and parents who fly off the handle everytime their precious little darling has their feelings hurt, so that can't be doing anyone any favors either.
I'm not going to downplay the problem of bullying. It can be as vicious as someone walking up to you and slapping you in the face with a brick for no good reason. It can have a lasting and damaging effect on teens and kids and sometimes, you just can't reason with a bully. Sometimes sticking up for yourself can make things worse when the bully is particularly malicious. But the media coverage in the last few years makes bullying seem this insane epidemic. Sensationalist news. We're living in a time where one's privacy is becoming more and more a memory, where anyone can put their entire life on the internet and tweet about whatever just happened to them in 140 characters or less.
So, to get to the point after all my rambling-- I really need to drink more coffee-- I think that, in most cases where the bullying is words and arguments, kids need to be taught to deal with it and to know that words are words and, in the case of bullies, words of idiots. Now if it's escalated to physical threats and violence and some kid really doesn't want to get into a confrontation of that type, go find help. Schools, parents, teachers, cops... there are plenty of people to go to. The worst cases? Prosecute. There needs to be a level of common sense in this situation; it doesn't have to be one extreme or the other as the media likes to portray.