People who identify themselves as witches do exist. As of 2014, there is a neo-pagan movement called "Wicca." Practitioners may be called witches, and the movement is associated with witchcraft, according to the Online Etymology Dictionary.
The source states that the term "Wicca" originated in Old English. At the time, it was a masculine noun referring to a male witch. Over the centuries, the term has come to be used to refer to a form of modernized witchcraft. While witches in this sense do exist, whether or not other types of witches exist is unclear. Because paranormal claims are difficult to verify, it cannot be said that any witches confirmed to exist have actual magic powers.