In the United States, Inauguration Day is celebrated on uneven numbered years every four years, on January 20th, the year following a presidential election.
Until then, Inauguration Day took place on March 4th, commemorating the date in 1789 when the federal government began operations under the US Constitution.
With the adoption of the Twentieth Amendment to the Constitution in 1933, Inauguration Day was changed to January 20th, and all incoming presidents have been sworn in on that day, with the exception of 34th President Dwight Eisenhower in 1957, 49th President Ronald Reagan in 1985, and 44th President Barack Obama in 2013 (as it fell on a Sunday). There are other exceptions of Presidents who took office following the death (FDR and JFK) or resignation (Nixon) of the sitting president, but their successors did not partake in an Inauguration Day.
The date changed because vote counting, travel time, and government formation used to take far longer. The lengthy transition to power proved to be both problematic and unnecessary as best exemplified with Lincoln, who faced the beginning of the Civil War with a separatist insurgence, or with FDR, who took office in 1933 in the midst of the Great Depression, and wasn't able to immediately tackle America's urgent economic challenges.
The Sunday rule is still observed: when January 20th falls on a Sunday, the Chief Justice (who traditionally officiates) privately swears in the President, and conducts the public ceremony the next day.