I manage several email marketing campaigns for clients and occasionally their subscribers request an email address be removed from the distribution list.
There are two ways to handle this: REMOVE and DO NOT MAIL.
Always use the DO NOT MAIL option, because if your client accidentally resubmits their name to be added to the database you have used the REMOVE option then they will be reinstated.
For example: client hands you a big stack of business cards to add to the database of people she met at a networking event. In the stack is the card of a person that has previously asked to be removed from the list. Had you used the DO NOT MAIL option to remove them in the first place, then that person will not be added back into the database.