First, there was the Corrupt Bargain of 1824, in which no presidential candidate received the required majority to win the general election, so the decision was handed to the House. The votes were split between John Quincy Adams, Henry Clay, William H. Crawford, and Andrew Jackson, who had the vast plurality of the popular votes. When the decision went to the House, the Speaker of the House (none other than 3rd place candidate Henry Clay!) convinced the House to vote for JQA, and in return, Adams made Clay his Secretary of State. The populists were furious, and Jackson was voted in as president for the next general election in a landslide.
Other less significant upsets are the election of Rutherford B. Hayes (president), George W. Bush over Al Gore (president), and more recently, David Brat over Eric Cantor (standing House majority leader). The latter may be the most shocking, considering that Representatives of the House are statistically speaking the most secure federal jobs that are dependent upon elections.
This submission has been removed because it violates the rule on poll-type questions. These poll-type questions do not lend themselves to answers with a firm foundation in sources and research, and the resulting threads usually turn into monsters with enormous speculation and little focussed discussion. “Most”, “least”, "best" and "worst" questions usually lead to vague, subjective, and speculative answers. If you'd like, you may PM /u/caffarelli to have your question considered for an upcoming Tuesday Trivia thread.