Remove @me.com and icloud.com.
If what you are asking is how to delete an Apple ID from Apple's servers the answer in short it that you can not. At least they do not have a simple process to do so. There is no way to remove an Apple ID from Apple directly from their associated websites, instead you have to call Apple support directly and see if they will assist you.

If you are worried about information that you have stored on Apple's database you can go into your Apple ID settings (https://appleid.apple.com/#!&amp;page=signin) and remove information you no longer want them to save.