For the most part, I try to ignore it if someone's causing me problems or at least act like it's not a problem at all. The one thing people want to see is you being bothered by something.
Otherwise, if it's someone I know and actually consider a respectable person (read: not doing things out of immaturity), I'll sit down and talk to the person to try to sort things out.
Either way, I don't like resorting to violence for several reasons:
1. After all the fighting, you still have the problem. I mean, if a person starts a rumor about you, the rumor will still be there, only with more bad words attached to it because you're not only (insert something here) anymore. You're also violent and rude, which starts a whole 'nother vein of potential insults.
2. The potential to add more trouble to the problem. While there's the example about the rumor and how a fight could add to it, I'm also talking about something a bit more serious. Like getting caught by the police (for assault and battery), a principal, your boss, whatever. And that's infinitely worse than any sort of petty problem you could've had to begin with.
3. It hurts. Stating the obvious, I know, but why would I put myself in danger for no apparent reason (except maybe self-defense at that very moment from a physical threat)?