GM
A Game Master is the person who adjudicates the rules and controls all of the elements of the story and world that the players explore.
A GM's duty is to provide a fair and fun game.
In some fantasy RP Gs the Game master is specifically called Dungeon Master referring to the original tendancy of the game to raid dungeons for treasure.
Some other games, in particular non-fantasy games, use terms such as Referee or Keeper.