President was the title given to the heads of state, usually of a republic, or the figure who presided over a governmental or corporate body. There were presidents on many worlds, including Gallifrey, Earth, Androzani Major, Fangoria and Theros. (TV: The Deadly Assassin, The Sound of Drums, The Caves of Androzani, PROSE: Warmonger, COMIC: The Therovian Quest)
On Gallifrey, the Lord President of the Time Lords was the head of Gallifreyan society. (TV: The Deadly Assassin) Androzani Major was similar, having a single president as the planet's lead official. (TV: The Caves of Androzani)
Throughout its existence during the American Civil War from 1861 to 1865, the Confederate States of America was likewise governed by a president. The only person to ever hold the office was Jefferson Davis. (PROSE: Blood and Hope)
By 2014, in times of crisis, UNIT had created a regulation whereby the Doctor would be officially appointed as the President of Earth in the times of extreme crisis as the only person everyone would trust with the defence of Earth, such as the Cybermen converting the dead, the apparent breakdown of the UNIT/Zygon peace treaty, and the mysterious appearance of the Monks' pyramid (TV: Death in Heaven, The Zygon Inversion, The Pyramid at the End of the World).