Chess originated in India as a simulation of battle, and quickly spread and became a popular pastime.  The history of chess is formed of much legend and uncertainty.  One such story is that the game originated in a feud between two warring brothers.  However, what is known is that a precursor of the modern game was being played in India in the seventh century AD, albeit with different pieces and rules.  There are numerous versions of the game throughout the world, particularly in Asia, and it is likely that chess is simply one of these, spreading from its origins in the Indian subcontinent to become one of the most popular strategy games in the world.

By the tenth century AD, the history of chess moved to Europe, and the game began to take its modern form, with rooks and bishops replacing the original Indian game pieces.  The game’s popularity spread far and wide, and competitive chess took off in the nineteenth century, with the first international chess tournament held in London in 1851.

http://en.wikipedia.org/wiki/Origins of chess

Were the rules of chess always the same?

The rules of chess have changed significantly over the history of its development.  Dark and light squares were only introduced after the game reached Europe in the tenth century or so, and prior to its arrival on that continent, the game used different pieces such as elephants and ‘counselors.’  Between 1200 AD and around 1475, the modern game took shape, with pawns able to move two squares on their first move, bishops acquiring newfound powers of movement, and the queen becoming the most powerful piece on the board.  Castling and en passant were also introduced into the modern game.  By the fifteenth century, the game had taken on a form that we would today recognize as chess.

http://encarta.msn.com/encyclopedia_761565896_3/Chess.html#s18

How did it become popular?

From India, it was natural that chess would spread outwards, as India was at the center of many of the world’s most lucrative trading routes.  The game quickly found its way to Persia, and when that kingdom was conquered by Islam, chess spread throughout the Middle East quickly.  Traders and returning Crusaders brought the new game with them, as well as the name ‘chess,’ which many believe is a mispronunciation of the Persian word for king, ‘shah.’  Chess sets were highly prized for their beauty and craftsmanship, and so the game had a social cachet as well.

http://www.mynetcologne.de/~nc-jostenge/