1. Daniel D. Tompkins (1817-25). Born on June 21, 1774, he is also one of the five youngest Vice Presidents. He served two full terms under President James Madison, and died three months after leaving office, on June 11, 1825, aged 50 years, 355 days.
2. John C. Breckinridge (1857-61). Born on January 16, 1821, he was the youngest Vice President ever when he and President James Buchanan took office. He only lived 54 years, 121 days, dying on May 17, 1875.
3. Garret A. Hobart (1897-99). Born on June 3, 1844, Hobart was William McKinley's first Vice President. His death in office, on November 21, 1899, cleared the way for McKinley to choose a new running mate in the election of 1900. That new Vice President, Theodore Roosevelt, became the youngest President ever when McKinley was assassinated in 1901. Hobart lived 55 years, 171 days.
4. James S. Sherman (1909-12). Born on October 24, 1855, Sherman died in office on October 30, 1912. His death came one week before the election of 1912, in which he was a candidate for re-election. His death, however, probably didn't have a major effect on the election, because former President Theodore Roosevelt was running for re-election against Sherman's President William Howard Taft (who had been Roosevelt's chosen successor). Democrat Woodrow Wilson took advantage of the split in the Republican Party to handily win the three-way race. Taft (and the deceased Sherman) came in third. Sherman lived 57 years, 6 days.
5. Chester A. Arthur (1881). Born on October 5, 1830, Arthur was Vice President for about six months. His President, James Garfield, was shot in July 1881, and died of the wound in September, vaulting Arthur into the Presidency. Arthur served his term, was not nominated for another, and then died on November 18, 1886, aged 57 years, 44 days. He is also #5 on the list of Presidents who died the youngest.
The youngest of the currently living Vice Presidents (all of whom are ineligible for this list) is Al Gore (1993-2001) who was born March 31, 1948.