ANSWER
William Howard Taft
The 1912 presidential election was an unusual three-way race between the Republican incumbent Taft, Democratic candidate Woodrow Wilson, and former president Theodore Roosevelt, running under the "Bull Moose" party after failing to win the Republican nomination. Feeling the pressure of two strong candidates, Taft broke with tradition and openly campaigned on his own behalf. Unfortunately for him, it wasn't enough. Taft finished a distant third behind Wilson and Roosevelt. Thus he became the only incumbent president to ever finish third in a bid for re-election.
Other trivia: Taft was the first president to have a car, and that last to keep a cow on the White House lawn. (The best way to get fresh milk in the days before reliable refrigeration.) He was also the only president to also serve as Chief Justice of the Supreme Court, the job he really wanted - it was his wife that urged him to run for president. Aside from John F. Kennedy, he is the only other president to be buried in Arlington National Cemetery. And he was fat - he was the heaviest president in US history.
WHO GOT IT RIGHT: Pete Daggett, Bob Milligan, Marc Quinlivan, and Ryan Scannell.