The peculiarities of early American voting procedure meant that although Washington won unanimous election, he still had a runner-up, John Adams, who served as vice president during both of Washington's terms. Electors in what is now called the Electoral College named two choices for president. They each cast two ballots without noting a distinction between their choice for president and vice president. Washington was chosen by all of the electors and therefore is considered to have been unanimously elected. Of those also named on the electors' ballots, Adams had the most votes and became vice president.
Although Washington's overwhelming popularity prevented problems in 1789 and 1792, this procedure caused great difficulty in the elections of 1796 and 1800. In 1796, Federalist supporters of John Adams cast only one of their two votes in an effort to ensure that Adams would win the presidency without giving votes to any of the other candidates. This led to a situation in which the Federalist Adams won the highest number of votes and became president, but Thomas Jefferson, the opposing Democratic-Republican candidate, came in second and therefore became his opponent's vice president.
In 1800, the system led to a tie between the Democratic-Republican candidates for president and vice president, Thomas Jefferson and Aaron Burr. This sent the vote to the House of Representatives, where Federalists voted for Burr instead of Jefferson, whom they despised. As a result, the Congressional vote ended in a tie 35 times before the Federalists decided to hand in blank ballots and concede the White House to Jefferson.
In 1804, the 12th Amendment to the Constitution ended this particular form of electoral chaos by stipulating that separate votes be cast for president and vice president.