Presidents may indirectly elected through an electoral college, or directly elected. The United States indirectly elects its president using an electoral college. Mexico and Brazil elect their presidents directly.
Additionally, some countries require that their directly elected president win a majority--either an absolute majority, or some large plurality--of votes.
The U.S. Founding Fathers decided on an indirectly elected president because they believed voters would vote according to parochial, state-based, interests, because they feared the "tyranny of the majority", and because they were concerned that the office could become too powerful with a direct mandate from the people. The Founding Fathers designed the elaborate and, at times misfiring, Electoral College to ensure that the president has broad support across the many states.
Nowadays, the Electoral College is often criticized as being outdated and contravening principles of majority rule. For more on the Electoral College, and proposals for its reform see our "Electoral College" page.
Of the 28 freest presidential democracies, 21 require the president to win with a majority of votes. Two more mandate presidents be elected with relatively high minimum pluralities. Only five allow pure plurality winners. One of them, the United States, permits the winner of the popular vote to lose the election through an Electoral College system. The 23 countries with majority and minimum plurality requirements all employ runoff elections. 22 use delayed runoff elections and one, Ireland, builds both rounds into one with instant runoff voting (IRV).