Simplistic version:

Played by two players, one playing black stones, the other white stones, placing a single stone at a time on unoccupied intersections of a 19x19 grid. The object to control more of the board than the opponent does. One other rule is that should a stone be choked off of friendly neighbors or have no adjacent intersections unplayed, it is removed from played or that intersection is unplayable.

Depending on the country and the year, the rules may change subtly, but the gist is the same. There are many different rule sets in existence: Japanese, Chinese, American, Korean and Taiwanese, to name a few. For a more in depth study of the rules of Go, please see the follow sites:

From the US Go Association (PDF)
More on the variety of rules
From the British Go Association
Flash Demo on more than just the rules

Alternative rule set for learning to play quickly and intuitively:
From Mindy McAdams