Ancient cultures, including those as varied as the Romans and the Hindus, celebrated New Year's Day on April 1. It closely follows the vernal equinox (March 20th or March 21st.)
In 1582, Pope Gregory XIII ordered a new calendar (the Gregorian Calendar) to replace the old Julian Calendar. The new calendar called for New Year's Day to be celebrated Jan. 1.
In France, however, many people either refused to accept the new date, or did not learn about it, and continued to celebrate New Year's Day on April 1.
Other people began to make fun of these traditionalists, sending them on "fool's errands" or trying to trick them into believing something false.
In 1752, Great Britain finally changed over to the Gregorian Calendar, and April Fool's Day began to be celebrated in England and in the American colonies.

France

The French came to call April 1 Poisson d'Avril, or "April Fish." French children sometimes tape a picture of a fish on the back of their schoolmates, crying "Poisson d'Avril" when the prank is discovered.

England

In England, tricks can only be played in the morning. If a trick is played on you, you are called a "noodle".

Mexico

In Mexico, the holiday is called "El Dia de los Inocentes", which is December 28. The day was originally set aside for Christians to mourn Herod's slaughter of innocent children. Today the holiday has a lighter, more "traditional" April Fools' tone.

Scotland

In Scotland, April Fools Day is two days long. The second day is called Taily Day, devoted to pranks involving the posterior. "Kick Me" signs can be traced to this observance. If a trick is played on you, you are called an "April gowk".