To supplement gitm's writeup above, what made Paul Morphy so great is that he was the first chess player to concentrate on the systematic, rapid development of his pieces. In essence, Morphy was the father of the modern chess opening.

Before Morphy chess players concentrated primarily on pawn moves, like trying to dig a trench before beginning a battle. What Morphy understood first is that by bringing out his minor pieces--- bishops, knights-- he could command many more spaces than his opponent. The combination of pawn and piece moves allowed him to bring much more presssure on the center more quickly, and to respond with greater flexibility than his chess opponents. His style in essence gave him an advantage of many tempos, or moves. Development permitted him to both build his own defensive structure while pressuring his opponent.

This made Morphy chess's first great innovator. It is a shame that Howard Staunton ducked him. Still, that evasion stands as proof to his brilliance.