A historical investigation of Presidential reelection efforts shows only three Presidents, who survived to the end of their term, chose not to attempt to run for reelection:
James K. Polk in 1848
James Buchanan in 1860
Rutherford B. Hayes in 1876.
Five Presidents who did not survive to run were:
William Henry Harrison, elected in 1840, dying in 1841.
Zachary Taylor, elected in 1848, dying in 1850.
James A. Garfield, elected in 1880, dying in 1881.
Warren G. Harding, elected in 1920, dying 1923.
John F. Kennedy, elected in 1960, dying in 1963.
Five Presidents wished to run for reelection, but failed to gain a nomination on any party line:
John Tyler in 1844
Millard Fillmore in 1852
Franklin Pierce in 1856
Andrew Johnson in 1868
Chester Alan Arthur in 1884
Two Presidents chose not to run after succeeding a President due to death, only having one full term:
Calvin Coolidge in 1928
Lyndon B. Johnson in 1968