It's really a decision that is unique to each family. The most common reasons parents may decide to get a credit card in the name of their child include:

For emergencies

Letting the child (probably a teenager) do their own school shopping
Purchasing lunch and other necessities while out with friends
For traveling (perhaps the child visits family members regularly)

When you are deciding whether or not to get your child a credit card, you'll want to think about their age and maturity level. An elementary school student has very limited knowledge of what money is and how people get money. On the other hand, a teenager often has a better concept of how money is earned and what it's used for, and could be taught appropriate use of a credit card.

Many parents like the idea of getting their teenager a credit card in order to start teaching them about financial responsibility. If this is your goal, then obviously you don't want to hand the credit card to your child and let them have at it! You'll need to spend some time discussing the reasons for the child to have a credit card, set limits, and discuss how payments will be made with the card. Will your teenager be responsible for paying back the charges made to the card? If so, be sure you and your child discuss this as well.

Alternatives to Credit Cards

What parents may want to consider instead of an actual interest-bearing credit card is a debit card. Setting your teenager up with a bank account with a debit card teaches them to spend money they actually have, rather than spending money and paying for it later. It is up to you how the bank account itself is funded, but some parents have set up “direct deposits” for their children's allowance- which the child accesses using their debit card.

A “Charge Card” is another good option for the younger crowd. While they can be used to charge purchases, you cannot carry a balance from month to month on the card and must make the payment in full each month. This will teach your child responsibility for “charging”- provided you don't just pay it off each month for them without some discussion or maybe requiring the teenager to use their part time job or babysitting money to make the payments.

If you decide you want to get a credit card, charge card, or debit card for your own child, be sure you look into the rules of such an account with the provider you want to go with. Some credit card companies restrict the “additional cards” to people of a minimum age; while others allow anyone of any age to be the secondary card holder. Same goes for charge cards. For debit card accounts, there are banks that offer youth checking or savings accounts with debit cards that are specifically geared to the needs of teenagers. That might be your best option for instilling financial responsibility in your children.

How to Use Credit Cards, Charge Cards or Debit Cards to Teach Financial Responsibility to Children

When getting a card issued in your child's name, it's important that you spend some time with the child teaching them the basics. Don't take for granted that they will already have this knowledge. If the goal is to use the cards for teaching financial responsibility, here are some things to consider:

Teach your children not to lend their cards to friends for any reason
Review bank statements together monthly and compare receipts with purchases made on the statement
Teach children to pay more than the minimum payment – and teach them why that's important!
Discuss what a credit score is and how it affects people in life