This page contains information regarding Star Trek: Picard, and thus may contain spoilers.
The President of the United States was the head of state and chief executive officer of the government of the United States of America. The President led this country by proposing and executing policy, and was also the Commander-in-Chief of the United States military. The President resided in the White House. (DS9: "Little Green Men"; ENT: "Storm Front, Part II")
In 2152, Trip Tucker, hearing that Mestral may have lived on Earth from 1957 until well into the 22nd century, reckoned that the Vulcan explorer would have lived through "what – thirty presidents?" The first two of these would have been Dwight D. Eisenhower and John F. Kennedy. (TOS: "The Cage"; DS9: "Little Green Men"; ENT: "Carbon Creek")
- George Washington: 1st President
- Andrew Jackson: 7th President
- Abraham Lincoln: 16th President
- Ulysses S. Grant: 18th President 
- Theodore Roosevelt: 26th President
- Woodrow Wilson: 28th President
- Franklin D. Roosevelt: 32nd President
- Harry S. Truman: 33rd President
- Dwight D. Eisenhower: 34th President
- John F. Kennedy: 35th President
- Lyndon B. Johnson: 36th President
- Richard M. Nixon: 37th President
- Jimmy Carter: 39th President
- Ronald Reagan: 40th President
- George H.W. Bush: 41st President
- William J. Clinton: 42nd President
- George W. Bush: 43rd President
- Joe Biden: 46th President
- Individual was referred to while serving in a capacity other than President (his previous service as a general in the Civil War).
Although the aired version of Star Trek V: The Final Frontier seems to imply that Sulu and Chekov are in Yosemite National Park with Captain Kirk and the others, a deleted part of that scene actually establishes that they are exploring Mt. Rushmore, which has by the 23rd century had the head of an African-American woman President added. The scene was never made a part of any cut of the film, though, so the addition to Mt. Rushmore is non-canon.
Thomas Jefferson, the 3rd President, was part of the deleted scene mentioned above. His quote "I have sworn eternal hostility against every form of tyranny over the mind of man." appeared on the dedication plaque of the USS Yamato in "Where Silence Has Lease".
According to the short story "Eleven Hours Out" in the anthology Tales of the Dominion War, the United States still exists as a political subdivision of United Earth as late as 2375, and is still led by a President.