Two sets of presidents share the same birthday: James K. Polk and Warren G. Harding on November 2 (1795 and 1865, respectively) and Andrew Johnson and Woodrow Wilson on December 29 (1808 and 1856, respectively). But for a twist of electoral fate in 1877, however, February 9 would have been another such shared-birthday: William Henry Harrison (1773) and Samuel J. Tilden (1814).
Though the presidency didn't really work out for either of these men -- one won the prize, then dropped dead, while the other had it stolen from him -- in terms of posthumous fame, they haven't done badly. They're fairly large footnote characters in American history for exactly those things, dying in office and being denied office.
But there's so much more. Harrison was instrumental in the settlement of the Northwest Territories, both as a military and political leader; and his campaign in 1840 anticipated much in modern US electoral politics. His party, the Whigs, "flooded the electorate with posters and badges extolling the virtues of their colorful, down-home 'log cabin and hard cider' candidate, the hero of Tippecanoe," notes the Harrison biography published by the Miller Center for Public Affairs at the University of Virginia. "In their image remaking of Harrison, the Whigs misrepresented him to the electorate. Harrison was actually from an established Virginia family, a learned student of classics, and a man who enjoyed luxurious living to the point that he was continually in debt. The Whigs' strategy worked. It became the first true use of political 'handling,' or public image-making, in an American presidential race."
As for Tilden, he didn't get to be the 19th president of the United States. (Or perhaps he could be referred to as the 19th* president.) But he did well in the rough-and-tumble of New York State politics in the Gilded Age. As corporation counsel for New York City and chairman of the New York State Democratic committee in 1871, "he seized the opportunity... to endeavor to fasten upon the principal city officials the crime, universally suspected, but of which there was no proof, of having corruptly embezzled to an enormous extent the moneys of the city," wrote John Biglow in the preface to Letters and Literary Memorials of Samuel J. Tilden (1909). "By a long and patient tracing of the multitude of accounts in different banks, he reached a series of results which, when compared, not only disclosed but conclusively demonstrated... the whole scheme of fraud."
Tilden played a large part, then, in the fall of Boss Tweed. Later, upon his death in 1886, Tilden also left part of his considerable fortune for the establishment of a library in New York City. Ultimately, in combination with two other libraries, it became the New York Public Library, one of the world's great libraries.