When raising your child, do you/would let them learn from their mistakes or stop them time after time after they do something wrong?

I've been to peoples places where the kids are just running around and playing everywhere and anywhere and climbing furniture. The kids have been on the verge or breaking or just plain breaking them and the parents do really do much and just say they will learn.
I'm not a parent so I don't know. I have heard that kids who are curious and touch everything and break things grow up to be smarter, but I don't think it's a proven fact.
What do you guys think?

I personally don't like brats. There is probably a point in which they won't understand what is right or wrong, but the second they learn to understand I will be a bit more strict.