I do believe that not only should young children be taught how to handle money, but to handle money responsibly. Meaning, I believe that it is more than just "Johnny, you helped mom and dad out with the dishes, cleaning up the living room, the laundry, and picking up your toys, so here is your allowance for the week."
Personally, I think it is about the responsibility of money. One way that I found interesting is that one family actually uses the monopoly money to help instill not only the appropriate use of money, but to provide an ongoing education of what it means to save, to be able to provide for oneself, and the ability to build good work ethics and financial stability that will become a harvest in their adult life.
I think it is a tragedy for any family to give into their children's demands of wants and those children have no concept of good work ethics, or financial understanding of what it means to have and not have.