Origins of 'Jack and Jill'

There are many theories as to the origin of the rhyme Jack and Jill. As with the origins of most nursery rhymes, most, if not all of these are apocryphal.

Norse Mythology

The story of Hjúki and Bil is about a brother and a sister who follow the personified moon, Máni across the sky. The story, written in the 13th century Prose Edda by Snorri Sturluson, tells of how, as they fetched water from the well of Byrgir, carrying the pail Sæg, Máni kidnaps them from the Earth. They are now immortalized on the face of the moon, and the pair personify the waxing and waning moon, appearing and disappearing one-by-one on the moon's face ("Jack fell down and broke his crown, and Jill came tumbling after"). Some have drawn a connection between the stories due to the similarities in the names and the actions of the two children.

The Rise and Fall of Louis XVI and Marie Antoinette

This theory can be disproved by the simple fact that Jack and Jill first appeared in print in John Newbery's Mother Goose's Melody in the 1760s, well before the French revolution. Many, however, continue to propagate this origin story. Louis and his queen ascend to the throne (up the hill) and Louis falls and is beheaded, and Marie soon after (broke his crown, etc.) The "pail of water" is usually not taken into account, though some have said that it is a metaphor for the royal couple trying to quell the fires of the revolution.

Charles I and tax reform

(quoted from wikipedia)

In the 17th century, King Charles I tried to reform the taxes on liquid measures. He was blocked by Parliament, so subsequently ordered that the volume of a Jack (1/2 pint) be reduced, but the tax remained the same. This meant that he still received more tax, despite Parliament's veto. Hence "Jack fell down and broke his crown" (many pint glasses in the UK still have a line marking the 1/2 pint level with a crown above it) "and Jill came tumbling after". The reference to "Jill", (actually a "gill", or 1/4 pint) is an indication that the gill dropped in volume as a consequence. A variant of this is that liquids (specifically alcoholic beverages) were watered down, hence, "fetch a pail of water."