Doppelganger

From Wikipedia.com:

A doppelgänger (help·info) is the ghostly double of a living person. The word doppelgänger is adapted from German doppel, meaning "double", and gänger, translated as "goer" (though in this context, the meaning is closer to "walker"). The term has, in the vernacular, come to refer to any double or look-alike of a person, most commonly in reference to a so-called evil twin, or to bilocation.
Alternatively, the word is used to describe a phenomenon where you catch your own image out of the corner of your eye. In some mythologies, seeing one's own doppelgänger is an omen of death. A doppelgänger seen by friends or relatives of a person may sometimes bring bad luck, or indicate an approaching illness or health problem.

Famous reports of the Doppelgänger phenomenon

Emilie Sagée was a schoolteacher in the nineteenth century whose Doppelgänger's public appearances were recorded by Robert Dale Owen after being reported to him by Julie von Güldenstubbe.
Guy de Maupassant recorded his own Doppelgänger experiences in his story Lui.
Percy Bysshe Shelley claimed to have met his Doppelgänger foreboding his own death.
John Donne, the English metaphysical poet, apparently met his wife's Doppelgänger in Paris, foreboding the death of his yet unborn daughter.
Abraham Lincoln told his wife, while shaving after his election as president, that he saw an image of himself in the distance fade away while shaving in front of a mirror. He believed this to mean he would be elected to a second term but would not survive.

Emilie Sagée
Robert Dale Owen was responsible for writing down the singular case of Emilie Sagée. He was told this anecdote by Julie von Güldenstubbe, a Latvian aristocrat. Von Güldenstubbe reported that in the year 1845–46, at the age of 13, she witnessed, along with audiences of between 13 and 42 children, her 32-year-old French teacher Sagée bilocate, in broad daylight, inside her school (Pensionat von Neuwelcke). The actions of Sagée's Doppelgänger included:
Mimicking writing and eating, but with nothing in its hands.
Moving independently of Sagée, and remaining motionless while she moved.
Appearing to be in full health while Sagée was badly ill.
Apparently also, the Doppelgänger exerted resistance to the touch, but was non-physical (two girls passed through the Doppelgänger's body).