In an interesting article the US Chess League attempted to classify different styles of players. Their list:
Technical: A technical player will usually play the same openings repeatedly and know them extremely well…they are hard to play against… almost all technical player's seem to have an incredible overall chess understanding. It's a very practical style of play…it's almost impossible to be a technical player, without being very strong, as it requires too much chess understanding for lower rated players to use successfully.
Positional Players: Postional players are more versatile in their opening choices and simply rely on their general chess understanding to find the right solution in all positions.
Attacking Players: Feel comfortable with the initiative. They want to be always attacking the opponent…some attackers don't even have to be great calculators, but instead just have a natural understanding of how to conduct an attack.
Calculators: Generally work very hard at the board. Even though their general chess intuition may not be the greatest, they make up for it by pure and raw calculation power. They try to always see one move further then their opponent, and are ready to pounce if you make just the slightest miscalculation.
Tricky Players: Repeatedly they will play moves that you didn't even consider and that just flat out look weird, to the extent that it may become very confusing for you… they are constantly looking for ways to trap and attack you.
Dynamic players: Usually pretty well rounded, but lean more towards the aggressive/tactical side. They often play enterprising openings and try to simply outplay you. They aren't scared to mix things up and are usually fighting constantly.
Practical: They understand that chess is a game, and the object is to do everything possible to win and not always to find the absolute best move. They usually will play openings they are very familiar with…these players often have serious holes in their theoretical knowledge. They just hope to get a reasonable position out of the opening without spending too much time…
Intuitive: A weird group of players. You get the sense that they simply understand where the pieces belong, whether the game is positional or tactical in nature. Their reliance on their intuition may sometimes be a weakness as they trust their instincts too much …
Logical: Try very hard to try to understand the position they are playing from a logical perspective. These players won't often try anything too unorthodox, however they also won't shy away from complications if they are necessary.
Young Players: Have not yet developed a sense of style. It's very rare that you will find a positional young player…
For a complete discussion visit their site.