From the wikipedia entry for “doppleganger”
Carl Sandburg's biography of Abraham Lincoln contains the following:
A queer dream or illusion had haunted Lincoln at times through the winter. On the evening of his election he had thrown himself on one of the haircloth sofas at home, just after the first telegrams of November 6 had told him he was elected President, and looking into a bureau mirror across the room he saw himself full length, but with two faces.
It bothered him; he got up; the illusion vanished; but when he lay down again there in the glass again were two faces, one paler than the other. He got up again, mixed in the election excitement, forgot about it; but it came back, and haunted him. He told his wife about it; she worried too.
A few days later he tried it once more and the illusion of the two faces again registered to his eyes. But that was the last; the ghost since then wouldn't come back, he told his wife, who said it was a sign he would be elected to a second term, and the death pallor of one face meant he wouldn't live through his second term.
(Sandburg, Carl. Abraham Lincoln: The Prairie Years. Harcourt, Brace and Co., New York, 1926. Volume 2, Chapter 165, pp.423-4)
This is adapted from Washington in Lincoln's Time (1895) by Noah Brooks, who claimed that he had heard it from Lincoln himself on 9 November 1864, at the time of his re-election, and that he had printed an account "directly after." He also claimed that the story was confirmed by Mary Todd Lincoln, and partially confirmed by Private Secretary John Hay (who thought it dated from Lincoln's nomination, not his election). Brooks's version is as follows (in Lincoln's own words):
It was just after my election in 1860, when the news had been coming in thick and fast all day and there had been a great "hurrah, boys," so that I was well tired out, and went home to rest, throwing myself down on a lounge in my chamber. Opposite where I lay was a bureau with a swinging glass upon it (and here he got up and placed furniture to illustrate the position), and looking in that glass I saw myself reflected nearly at full length; but my face, I noticed had two separate and distinct images, the tip of the nose of one being about three inches from the tip of the other. I was a little bothered, perhaps startled, and got up and looked in the glass, but the illusion vanished. On lying down again, I saw it a second time, plainer, if possible, than before; and then I noticed that one of the faces was a little paler — say five shades — than the other. I got up, and the thing melted away, and I went off, and in the excitement of the hour forgot all about it — nearly, but not quite, for the thing would once in a while come up, and give me a little pang as if something uncomfortable had happened. When I went home again that night I told my wife about it, and a few days afterward I made the experiment again, when (with a laugh), sure enough! the thing came back again; but I never succeeded in bringing the ghost back after that, though I once tried very industriously to show it to my wife, who was somewhat worried about it. She thought it was a "sign" that I was to be elected to a second term of office, and that the paleness of one of the faces was an omen that I should not see life through the last term.
Lincoln was known to be superstitious, and old mirrors will occasionally produce double images; whether this Janus illusion can be counted as a doppelgänger is perhaps debatable, though probably no more than other such claims of doppelgängers.