Obviously you can't ignore some behavior. You have to pick your battles. Some things are best left ignored if they are attention seeking behavior. If you don't pay attention to it, the child will learn that is not an effective way to get your attention.
For example: Let's say your kid is in the back seat of the car kicking your seat to get your attention. You can say "Gee, if you want my attention, then you need to use words to let me know what you are needing. If you kick my seat, I will not respond to you". And then, don't respond to it. You will have to grit your teeth a bit here, because it will drive you nuts. Eventually the child will notice that they don't get any attention for this.
Obviously, you can't ignore a child running into the street. That has to be met with different consequences becuase it is not attention-seeking behavior. It is dangerous.
We need to remember that discipline and punishment are not the same thing. Discipline refers to the manner in which we raise our children and the structure we set for them. These are the guidelines for behavior. What I have found is that natural consequences are very effective in altering behavior, as well as stating expectations. Children function best when the consequences for their actions are predictable and consistent.
For example: If i tell my child to pick up her toys in the yard so that I can mow after lunch and she does not do it, then barbie dolls get their heads mowed over by the lawn mower. "Look, I see that your toys did not get picked up, and as a result, they were ruined by the lawn mower. I am so sorry that happened".
Another Example: We are going to the store, and while we are there I expect you to sit in the cart and behave yourself. That means no yelling, and no telling me "I want, I want". If you can remember this, then we will go to the park afterward" The child knows what is expected.
My biggest problem is caving in to tears. I hate it when y children cry, but I really have to remember to stick to my guns, or discipline is ineffective.
This is what works for me.