So... I'm going to go against the flow here and say that I'm wholly against using violence [i]just[/i] to 'teach people a lesson'. I mean, using violence to stop someone from harming a third person at this moment makes perfect sense to me; it's not like mostly anyone will listen to rationality in the heat of a fight anyway, regardless of the reason of said fight. This also includes the somewhat over-the-top tyrant argument; I can completely understand using violence to break up a spree of abuse. However, when such immediate danger is not present, using violence against someone will more than likely only cause them to be more pissed off. The underlying problem, the reason that they're acting out in the first place, has not been fixed at all. In fact, it might very well reinforce their thought pattern of "Might makes right." Not to mention Harris's note that, in this day and age, using violence against a school bully could just cause said bully to bring a weapon next time.

Mind you, I am NOT saying we should just say "Bad Peter, you shouldn't punch Jimmy in the face, that's not a nice thing to do", then simply walk away. What I am saying is that there are other ways to stop people like that. When we're speakig about adults, throw them in jail for the crime of physical abuse and force them to undergo therapy. If it's still a child (Which, as far as I care, would be anything below 16 at the least, possibly anything below 18 even), punish them by taking away their priviliges and, if it's more than a momentary outburst, force them to undergo therapy -- which, of course, should be age appropriate. The main goal here is to, especially with children, make them understand that using violence is flatout unacceptable in current society and to show them what effects their actions have on their victims. 
Now, I hear you thinking; 'But what if the guy is a true sociopath?'. Well, in that scenario I doubt that using violence will magically cure said sociopathy. They tried that in the past, and generally it only made things worse, further screwing up the person in question. The best we can do is to just protect society as a whole and cast them out/throw them in jail. 

Anyway, short version: 
Using violence to stop something that's happening right now: Okay, within reason (No bringing a fully automatic assault rifle to a school bully, to give an extreme example)
Kicking someone while they're already on the ground, or so to speak: Not okay.