A great way that my sister does it is she gives the brats a monthly allowance...when it's gone--it's gone. Want more? Too bad, so sad. You should have budgeted better. It took a few months, but now they have money left over at the end of the month for savings.
If I were to use her basic framework, I would do this:
Figure out a fair price, and what they would be responsible for with that money (entertainment, clothes?, hair cuts and personal care items or will it just be for movies and CDs). Choose an amount based on the preceeding.
After an amount has been agreed on, offer up "bonuses" paid a month in arears. If they meet all of the pre-determined requirements, they get a small bonus (reqs could be not getting in trouble, grades of ? or better, responsible attitude etc).
Make them see that it is like a pay check--you get what you get, and that's it. No begging for more money (with the exeption of "raise talks" every year or 6 months).
If they learn to budget now, maybe they won't have as much credit card debt later in life...