The chart above (from the NY Times) shows how successful third-party candidates have fared in presidential elections over the last century. Of the five most successful candidates, three helped the party on the opposite side of the political spectrum win the White House.
1912: Former Republican President Teddy Roosevelt, unimpressed with his Republican successor's term in office, attempts to win the White House as a member of the Bull Moose Party. The result: President Taft comes in an embarassing third, Roosevelt a strong second, and Democrat Woodrow Wilson becomes president.
1980: Liberal Illinois Republican John Anderson runs a independent campaign to the left of President Jimmy Carter and Republican candidate John Anderson.
1992: Texas billionaire Ross Perot bankrolls his own bid for the presidency, helping incumbent George H. W. Bush tally an abysmal 37% of the popular vote and lose the White House to Democrat Bill Clinton.
What could this mean for a potential Bloomberg candidacy? It's hard to say at this point, but I stand by my comment from earlier this morning: He's bound to hurt the Democratic ticket more than the Republican ticket.