Richard Bartle's Taxonomy of Player Types

Richard Bartle has been designing online RPGs for years, defined the four types of game players:

Achievers - want to achieve the goals of the game. Primary pleasure is challenge.

Explorers - want to get to know the depth and breadth of the game. Primary pleasure is Discovery.

Socializers - are interested in relationships with other people/players. Primary pleasure is fellowship.

Killers - interested in competing with and defeating others. Primary pleasure is challenge, mixed with destruction.