We got our son a credit card when he was a junior in college. It was with Bank of America, and it was in his name and mine, so it piggybacked on our credit but allowed him to build a credit history, too. (He also has a couple of small loans for college, some subsidized, some not.)
He has now graduated and just took a job, so we went car shopping. Because he had the credit card, and because we was diligent in paying regularly, he had excellent credit and was able to qualify for a new car loan even though his job doesn't start for a couple of weeks. It really gave him a leg up as he is starting his life as a self-supporting (I hope!) adult.
The downside to the joint card is that it can affect your credit, too, so you have to watch the credit limit on the card (it affects your credit-income ratio) and if the child is not responsible with the card, you are on the hook and your credit rating can be affected if he/she is late on paying bills, etc.
