Facebook tags link your profile to a piece of content, such as a photo or status update, created by a friend. If you are unhappy with a tag, deleting it is easy. A "Remove Tag" link appears beneath the content you are tagged in, and clicking it will immediately remove the tag forever.
When you remove the tag from a photo or news feed post, the content remains on the profile of the person who posted it. Removing a photo tag will eliminate your name from beneath the photo; similarly, deleting a tag associated with a location check-in erases your name from the post entirely. You cannot delete the photo or post, however, because it does not belong to you. If a friend has tagged you in a news feed post, removing the tag only takes away the link of your name -- regular text displaying your name will still appear in the posted item.
Your Profile Copy
Each time a friend tags you in a photo or post, a copy of the item is placed on your profile. An update shows up on your wall, and photos are saved in the "Photos" tab of your account. When you remove a tag, your copy of the photo or post is deleted; visitors to your profile will see no trace of the photo, status update or location check-in that you were once tagged in.
The friend who tagged you in a post or photo is never notified when you remove a tag of yourself. Since the friend created the content that was originally tagged, however, she may notice that your tag no longer exists. Since you are no longer associated with the content, you will no longer get notifications regarding comments that are made beneath it -- even though you are still in an image, you will not see what people are saying about it.
Facebook friends always have the right to tag you in an image. As of June 2011, you cannot stop someone on your friend list from tagging you. If you tire of repeatedly removing the tags applied by a particular friend, Facebook suggests removing her from your friend list, which will revoke her ability to tag you. Go to the "Customize Settings" section of the "Privacy Settings" menu to stop friends from tagging you into places.