I would definitely start with one of those pre-paid one before giving them an actual credit card. I think that it might be a good way to teach children about money if instead of giving then a cash allowance, you set a bank account for them and give them a debit card - so they can either spend the money or save it for something big. I think you can start that at about 12-14 depend on the maturity of the child.

as they grow up, give them more money every week, but also expect them to pay for some of their expenses like bus \ train pass, lunch money, new cloths, phone bill (also a good way to teach them that talking for hours on the phone is not free) school books and so on.