There really isn't anything wrong with humoring small children and some teens would like to quit asking their parents for handouts and gain some sort of feeling of independence.
Clearly keep it so they aren't working full time jobs since they are just kids who have school and all that jazz but if they truly want to, no parental influence, then why not let them?
I see so many people here belittling the concept but some kids and/or teens would like some cash they can burn and buy stuff they want without having to wait for their Christmas or Birthday card from Grandma with a check inside.