Having an Apple ID is a prerequisite to do just about anything related to Apple services. If you want to buy music on iTunes, download apps in the App Store, or use iCloud, you must have an Apple ID.
A few years ago, linking a credit card to an Apple account was mandatory. But Apple has changed its stance and has been letting users create an Apple ID without a credit card for a while now.
Whatever your reason might be to do so, we are going to show you how to create an Apple ID without a credit card...