Why do we GM?
Why do we spend hours of unpaid time to create worlds? Why do we make the decisions we do during game sessions? Why do we submit to the scrutiny of our friends and peers in attempting to make a seamless, enjoyable experience out of a set of rules, some abstract numbers, a handful of dice, and hours of talking and armwaving?
I can think of a few general style buckets for GMs to fit into, based on where the most enjoyment or satisfaction comes out of the game. It's a work in progress based on what I enjoy about GMing, so hold on to your hats...
Gets enjoyment from creating the world or society. This GM can tell you the entire history of the royal bloodline and show you the map of every city known. Characters who start asking questions and doing research make this GM's day, because he can finally showcase all of his hard prep work.
Gets enjoyment from creating situations or scenes. Where the Historian creates the world in excruciating detail, the Plotter creates situations for the characters to deal with. The Plotter's creed reads, "It ain't where you are, it's what you do that counts."
Gets enjoyment from playing the part of all the NPCs. Actors may have started out as frustrated stage actors, or they may be slightly schizophrenic. Actors typically portray characters with different voices, mannerisms, and body language. They typically know their NPCs inside and out and are entertaining to watch as they switch between characters.
Gets enjoyment from manipulating or outthinking the players. Puppeteers analyze the players (and how they will probably portray their characters) and design scenarios that push hot buttons. Interpersonal and social conflict holds a special place in the Puppeteer's heart. It's a dangerous road to walk, but an accomplished Puppeteer really gets the players immersed in the game.
Gets enjoyment from actually running the game and creating things on the fly. Improvisationalists may come to a game with a few vague ideas about plots, then flesh everything out as they go along. They love playing gedankengames where everything exists only in people's thoughts and not anywhere on paper. My favorite extreme example of this is the world's simplest LARP: the players create the entire world/game/story, but they don't know they have that power at the start of the game. GMs continually ask, "Well, what do =you= think this widget does?" And the player always answers correctly.
Gets enjoyment from mastering the mechanics of the game. There's a certain amount of pride in being a walking rulebook. Mechanics typically run the fastest combats, and some can calculate all needed modifiers in their heads such that the players simply need to roll the dice and let the Mechanic figure it out. Mechanics also love homebrew rules and "systemless" games.
Gets enjoyment from entertaining the players. It doesn't matter what else happens in the game as long as the players have fun. Socialites tend to focus on factors outside of the game itself, such as buying munchies, providing comfy chairs, or giving character-coordinated dice as game rewards.
This list is far from exhaustive or even accurate. Please feel free to dispute these categories or add new ones based on your own experiences.
What gives you the most satisfaction when running a game?