Is it normal I don't punish my kids?

I think that's the ideal way of dealing with kids.

I'd like to point out that discipline is not the same as punishment, though. Punishment is a form of 'negative' discipline.

You're right when you say that punishment is often a knee jerk reaction, but not always.

I use a mix of disciplinary techniques. For example, at work last night, the three year old smashed me in the face with a piece of train track. He's not a violent kid, he just thought it would be funny (it wasn't...hah). So I told him that it hurt, it wasn't behaviour I expected, and I wanted him to stop. He did it again, and I warned him that the consequences of his actions, should he do it again, would be that the train set would be packed away until tomorrow. He did it again, the train set went away.

'Consequences' are used as discipline in two ways - logical (basically letting the direct result of the behaviour going unchecked to serve as punishment - ie if you keep doing that, you will get hurt and it will be unpleasant) and I forget the proper terminology for the other type (ie my above example with the trains).

I don't agree with physical punishment, though I will physically remove a child (gently) from a situation if needs be, to protect them or another child/person/animal/myself from them being harmed by the child's behaviour, or if the child needs to be removed from stimulus in order to calm down enough that they can discuss the situation (where age appropriate).

I hope that made sense, I just woke up.