I think showing respect is like treating the child like any other person. Recognizing his/her feelings, giving explanations (instead of "because I said so") for any rules/actions/punishments etc. It is different from giving in to his/her every requests. If he/she is throwing a tantrum in order to get his way, a parent should teach him/her the proper way to ask for something. This does not mean that the parent is not respecting his/her child.
Just my two cents worth.