One of the most important lessons you can teach your children are how to manage money. Many children reach the age of 18, begin receiving credit card offers, and have had no real experience handling money. Teaching children from a young age how to properly manage their money and the importance of savings is a lesson that will stay with them throughout their adult lives.
Whether you choose to give your children a weekly allowance just for being part of the family, or you require your child to earn the money through their chores, a weekly allowance can be effective for children starting as early as the age of four or five. Work with your children a little each week to teach them how saving a percentage of their earnings each week will grow over time, and how to divide the rest so that there is some money to spend and some to give to charity.
If you divide your children's money whenever they receive it - for birthdays, holidays or the $5 bill grandpa insists on giving junior every time he comes to visit - the children will learn quickly to be responsible with money.
As your children get older, you can start giving more information. Teaching a child that their money can grow through interest when saved in certain bank accounts will get them interested in the value of money. Allow your children to spend a portion of their money so they can learn the value of a dollar - that dollar might buy a candybar but not the video game they've got their eye on. You might want to encourage the child to set up a separate envelope or jar to save money for the more expensive toy or game they want, instead of simply buying it for them. Teaching a child to save for something they want is valuable and just might help them avoid buying on credit cards when they get older.
When your children reach their teen years, you might consider increasing their allowance and having them contribute to some of their necessity expenses, as well - things like car insurance, clothing, school supplies, etc. It will promote responisble financial habits that they will need when they go off to college or move out on their own.