Because you asked such a good question up front I'll allow myself to be drawn in... ;)
If reinforcement doesn't work (which actually means you haven't found the right reinforcer yet or you are doing something else wrong) and the behaviour is unacceptable you can use punishment, of course. Punishment is either giving an aversive stimulus or taking away a pleasurable one. A standard punishment is time-out. It works pretty well most of the time if you use it properly - but most people don't understand how to use it and so it fails.
Here's an example for a kid around 6: kid is hitting other kids. That's bad and we need to stop it ASAP. Reinforcement is not appropriate just yet so we are going to use punishment to extinguish the bad behaviour (hitting others). We immediately remove the kid to a totally non-stimulating environment (usually somewhere like an empty room) and set up rule governed behaviour by saying something like: 'you hit Johnny and that is not allowed. You are in time-out for X minutes, sit here quitely and don't move. If you move from the chair or make a noise the time starts again' The kid stays in time out for X minutes, but if they break the rules (move, speak, whatever) the time restarts.
In case you are wondering how that is punishment; being ignored while others are playing or whatnot is extremely aversive to young kids. Don't underestimate how punishing time-out can be to young ones if it is done properly. You have to be careful not to over do it.
When the kid has behaved properly in the time-out area for X minutes they can come out. Usually then get the kid to explain why they were in time out and what the correct behaviour is (ask for the toy, play nicely, don't hit others, whatever). Then, and this is really important, the very instant that the kid displays anything like the correct behaviour we reinforce that to the max (with praise, a sticker or whatever you are using).
Other punishments can be things like removing access to things like toys, TV time or whatever. There are lots of ways to apply punishment, but we usually only want to use it for behaviour that must be stopped ASAP - so things where the kid could get hurt, or hurt someone else are usually the go. Remember that the definition of a punishment is that it reduces a behaviour. Reinforcement increases a behaviour - that's why we want to reinforce them as soon as they start showing signs of doing the right thing.
There are whole books and lifetimes spent researching this stuff, so what I've posted is a drop in the ocean of the theory and application. As I'm just riffing this off the top of my head I may have missed something. My intent is not to provide the textbook solution, but to point out that we can use punishment that is not violent or physical - and has the added bonus of giving a much better model to kids on how to behave.
Also, I'm not an author or professor, so my explanation is not perfect. There are lots of good resources for this stuff both online and in text. If you are interested I can post some good ones.
Imagine the model you would set up by hitting a kid as punishment for hitting someone! Can you see that it makes no friggin' sense to do that?
Cheers,
Adam

