Yes, you do. All apps, music, movies and books downloaded from the iTunes store require the use of an Apple ID. Typically, a credit card is attached to this account as well to make the purchase of items convenient and easy.
However, there are times when you may NOT want to attach a credit card such as for "library owned" iPads, etc, but still want patrons to be able to download free apps. Apple has detailed how to do this in their support article here: