Child support payments aren't meant as a punishment for the parent who has to pay them. Instead, they are meant to help cover the expenses for the child. As you can imagine, this is important because rearing children is expensive. There isn't any good reason for one parent to have to shoulder the entire cost.
When you pay child support, you have to give the money to the other parent. They are the one that purchases the items the child needs, so don't assume that you are actually giving them free money. In fact, one thing that might cause a misunderstanding is that child support money can be co-mingled with other household funds. It is easy to misinterpret where the money is going because of this.
The child support payments are meant to cover things like shelter, food, clothing, school fees, fun activities and any other expense the child has. With almost no exceptions, the money that you pay isn't going to cover all of those in full. The other parent will also have to use their own funds as well.
Another issue that can arise is the shared bills that you might not want your child support to cover. Remember that your payments can be used to pay any bill that benefits the children, including mortgage or rent, as well as utilities.
Typically, you don't have to worry about where the support payments are going as long as the kids are taken care of. The only time the court will likely weigh in is when the kids are being neglected or don't have what they need to survive.