There are as many different kinds of Games Master as there are people willing to run games for people but they can, nonetheless, be streamed into a number of different types, depending where their focus on the game rests. If you're a player it helps to know what sort of Games Master you have so you can have realistic expectations of the game. If you're a Games Master identifying what sort of GM you are can help you identify your strengths and weaknesses and play to them or overcome them. Here's a few of the more recognisable ones:

Auteur
"The artist doesn't have time to listen to the critics. The ones who want to be writers read the reviews, the ones who want to write don't have the time to read reviews." - William Faulkner

The Auteur has an idea and you're privileged enough to be along for the ride. The Auteur isn't a railroading Games Master in the traditional sense but, rather they have a story to tell and if your irritating player actions get in the way, then they'll get ridden roughshod over. If they add to their idea then that's different, they might get incorporated and run with. The Auteur wants everything to be perfect, to shine light on their idea and for the game to be one of the best ever. If you all get on then this may, indeed, happen. If the player's tastes and ideas differ from those of the GM then you may be in trouble.

Advantages: The Auteur tends to put a lot of work and thought into their games and they're often great, so long as you don't go against the flow too much. The Auteur is unlikely to run out of interest in their own project and so you're pretty much guaranteed the game will run on through to its conclusion.
Disadvantages: The Auteur wants to do everything and they may include playing the player's characters, or at least interfering with them to the extent that they're unrecognisable to the player's original intent. You're also very unlikely to get a lot of leeway in playing the game and while not on rails per se, you're at best on a fairly narrow path.

Autocrat
"Dictatorship is without a doubt the most satisfying form of government...as long as I'm the dictator." - Phil Stromer

The Autocrat desires total and absolute control over the game and will brook no argument, no rules-lawyering and no complaints. They'll probably be quick to chuck people out of the group for being 'disruptive' and arguing their calls and they get off on being 'in charge'. They may even see the Games Master's role as being adversarial in a decidedly old-skool fashion.

Advantages: The Autocrat's game will tend to be organised and efficient, you'll get a lot of gaming done, albeit on their terms. They know how to keep order at the gaming table and to prevent others from spoiling the game.
Disadvantages: You can never quite be sure whether what you do while playing is going to offend and goofing off, half the fun in a lot of games, is less likely to be tolerated.

Captain Play-Doh
"Too little liberty brings stagnation and too much brings chaos." - Bertrand Russell

Captain Play-Doh is whatever you want him to be. You want to play a tense Lovecraftian horror using Bunnies & Burrows? You go it. You want to play a sentient otter with Jedi mind powers in D&D? No problem. Captain Play-Doh is an amorphous mass shaped almost entirely by the desires of the players which can often lead to games that are such an incoherent mess that anyone new joining the group wouldn't have the barest hint of a clue as to what the hell was going on.

Advantages: Whatever you want to play they're up for. Provided your gaming group isn't too wild and crazy (in different ways) this can help ensure everyone has fun and a GM with some flexibility is good for helping everyone get on and get their kicks from the game.
Disadvantages: If your group isn't coherent or of similar taste then you're going to end up with a growling Frankenstein's Monster of a game. Without a backbone Captain Play-Doh is unlikely to stick up for the things that they find fun or to be able to apply some necessary discipline to the game.

Enthusiast
"If you aren't fired with enthusiasm, you will be fired with enthusiasm." -  Vince Lombardi

The Enthusiast is dead keen on something. Perhaps it's Star Wars, Star Trek, Babylon 5 or The Lord of the Rings but it could be something much more obscure, like bats*. Whatever it is they're devoted to it, enthusiastic about it and are a die hard fan. While they know everything about it and can produce games and adventures of startlingly complex subtlety and depth on this subject, outside of it, not so much.

Advantages: Within the paradigm of what they know you won't find a better GM. Even better, everything they do will fit within that universe and no matter how obscure you go, they should know what you're talking about. This is even better if their enthusiasm is for a particular game that you all like to play.
Disadvantages: Outside of their favourite subject the Enthusiast isn't so enthusiastic and their performance will be lacklustre or, even worse, they'll start introducing things from what they do know into games that they don't like so much. AT-ATs as dungeons for example, or even worse.

Homebrew
"He who builds a better mousetrap these days runs into material shortages, patent-infringement suits, work stoppages, collusive bidding, discount discrimination - and taxes." - H. E. Martz

The Homebrew GM never does anything by the book. They build their own games either from scratch or by cannibalising the bits they like from other games and roughly nailing these pieces together and calling them a game, but a game that only they really understand. The Homebrew is a bit different to the professional games designer, who may be looking for playtesting. The Homebrew GM isn't interested in creating a working, professional product so long as their Rowland Emett-like game system does what they want it to do.

Advantages: You'll end up with a system and a game perfectly suited to your GM and the kind of games they like to play as well as their game world. At least they'll think it's perfect and that counts for a lot.
Disadvantages: You're unlikely to understand the system, so they could be just making things up for all you know. Whatever system there is, is likely to change from session to session, constantly pulling the ground from beneath your feet.

The Long Haul
"As you journey through life take a minute every now and then to give a thought for the other fellow. He could be plotting something." - Hagar the Horrible

The Long Haul Games Master is in their element with epic, long-term campaigns rather than individual adventures. They crave the extended story, the slow build up, the reveal and the intricacies and attachment that come with longer games. This long term view covers almost everything they do, meaning that individual adventures can cover... not very much ground.

Advantages: If you have the time and energy to invest in a long term campaign then these are the perfect Games Masters to have. They appreciate character development and if the games are slow to get going, the eventual payoff is worth it.
Disadvantages: If it's a one-off game you're after the Long Haul can be worse than useless as by the time the game gets anywhere you have to wind up the session, so you end up with a ton of different campaign starts that never go anywhere.

The Mayfly
"There are three side effects of acid. Enchanced long term memory, decreased short term memory, and I forget the third." - Timothy Leary

The Mayfly is the opposite of the Long Haul. The Mayfly is a firecracker chain of ideas and enthusiasms but none of them ever, really, seem to amount of much. The constant flow of ideas and distractions pulls them in all directions and makes them a fount of novelty but none of it ever really seems to stick.

Advantages: If you're after a one-off game the Mayfly is your man. Their scattershot of ideas is bound to get a few good hits and if you're really lucky you have another GM in your group who can take some of these good ideas and run with them.
Disadvantages: Even if you start a campaign the Mayfly is likely to lose interest and either change the game you're playing in some way or to want to change to an entirely different game.
Disadvantages:

Referee
"A judge is a law student who marks his own examination papers." - H. L. Mencken

The Referee sees the position of the Games Master as like being 'the guy who knows the rules' in a boardgame. They're there to officiate, to see that the rules are applied fairly and evenly and that the scenario is followed. While they're fair they're also likely to be fairly uncreative - at least where the rules are involved. A style of GMing that has largely fallen out of favour.

Advantages: You're going to be able to get a fair showing in the Referee's games but since most GMs bias in favour of the players, that may feel like they're picking on you rather than being fair. The Referee is going to know the rules though and you're unlikely to have huge pauses in the game while someone looks up a rule in the book.
Disadvantages: Referees tend to be the people who buy modules, so you may well find yourself stuck on rails when it comes to actually playing through an adventure. You're also unlikely to get away with any creative rules bending, even if it makes perfect, logical sense.

*Srsly, I felt really sorry for the guy but it was a non-starter.