According to the AICPA (American Institute of CPAs) the average allowance for an American kid is $15 per week. Doing this is a great way to get your kid on the road to budgeting or the very least keeping tracking of where it goes. I can't tell you how many brilliant professionals that I talk to that have no idea where their money goes.
In my opinion, an allowance should consist of 2 parts. The base salary, which is derived from chores and a bonus, that is derived from their grades. I'm fully aware that this is a contentious issue when it comes to "paying for grades" but the fact of the matter is that american children are required to go to school now. So you might as well incentivize them to do well.
From the beginning they should be taught to segment their allowance into the 3 main departments that adults have to. They should segment 10% of their income to retirement, have 6 months worth of "expenses" (however you want to come up with that number) so that they know the idea of an 'emergency fund', and the rest could be used for whatever they want.
Teaching delayed gratification should also be introduced. They should be taught the difference between wanting a candy bar and the new video game that they've been eyeing for the past 6 months. You want a candy bar? Pay for it out of your allowance. You want a $100 video game, but you don't have the money? You need to save for it until you do. There are no credit cards in kindergarten.
Don't eat the marshmallow kid!