An interesting statistic is how many Presidents have been nominated for President more than twice, as well as whether there were any Presidential nominees who lost the White House, but were nominated more than twice.
The list of Presidents who were nominated more than twice includes:
Thomas Jefferson (1796, 1800, 1804)
Andrew Jackson (1824, 1828, 1832)
Martin Van Buren (including the Free Soil Party nomination in 1848 along with 1836, 1840)
Grover Cleveland (1884, 1888, 1892)
Franklin D. Roosevelt (1932, 1936, 1940, 1944)
Richard Nixon (1960, 1968, 1972)
The nominees who were chosen more than twice were:
Henry Clay (1824, 1832, 1844)
William Jennings Bryan (1896, 1900, 1908)
As one can see, this is a very short list, indeed!