Teens want and need the independence of being able to make some of their own decisions, and an allowance can be a great way to give them that responsibility. They can learn something about budgeting (if I want that new computer game I'll have to save up; if I spend my allowance on the first day, I won't have any left) and have the freedom to choose what to do with their money.
The biggest question when setting your teen's allowance is what is the allowance supposed to cover? For many kids, especially younger ones, it's money for extras like snacks, games and trinkets. A rough guide for this type of allowance is $1 a week for each year of the child's age. At the other extreme, the allowance is meant to cover clothing, haircuts, entertainment, school lunches and the like. In this scenario, you'll need to take the time to plan a reasonable budget (preferably with your teen's input) to cover the child's needs and a least some of his wants. Be clear up front about what your teenager is going to have to cover out of his own money, and in what cases he can turn to you. Will you buy school supplies? Will you provide the money for gifts for family members? Let your teen know whether he'll be able to borrow against future allowances.
It's a good idea to encourage -- or even require -- your teen to save some of his money. Some banks have teen- and parent-friendly accounts, or you can use a piggybank or a home-made ledger of money put aside. You may also want your teen to give to others; talk together about charities and worthy institutions that he can donate to, and make a regular ritual of giving, whether weekly, yearly or something in between. Ensure that the allowance is high enough that your teen still has discretionary money after saving and giving.