Check out Jon Peterson's post on Player Typologies.
Well, ain't that something...
The more things change, the more they stay the same.
Nothing new under the sun... just certain points of view...
Addendum: Below is the post that went with it, from May 2009.
It is hardly complete and of course, completely debatable. I never really found the styles of Gygax and Arneson to be incompatible; they were merely along different points on different axes, and really both fall within the broad grouping under "High Adventure." That Gary advocated more along the lines of pure Adventure, while Dave emphasized the Role-Play aspect, does not mean their philosophies were at odds.
A few definitions are in order:
The Adventure element of gaming refers to the Character or party of Characters going forth and making their way through a setting, having adventures, killing monsters, looting and pillaging, and generally doing what adventurers do, regardless of whether the Players are emphasizing the Role-Play or Roll-Play aspect of the game. However, what is certain is that though there is a campaign setting, and the Game Master may even have some over-arching plot points and ideas for what is going on behind the scene, it is the PLAYERS that drive the game by their desire to have Adventure. In essence, Adventure gaming isn't about the destination, it's about the journey there... and there may very well be no "there" toward which one is striving.
The Narrative element of gaming is almost, but not quite, the reverse. While all the same things may occur in a Narrative game, the overarching interest of both Players and Game Master is the telling of a story within the pre-existing milieu created by the Game Master (and quite often, with the assistance of the Players). Often there is a Goal, and specific Antagonists, and all the other bits and pieces that come into play through the nuts-and-bolts concepts of the literary end of things. In essence, Narrative gaming is all about where you are going, and getting there in the most apropos and character-driven method possible.
Role-Playing gaming emphasizes the Player taking on the Role of the Character; at the furthest end of this axis, you are actually dealing with full-immersion into the character, with reams of background and names of allies and enemies, likes and dislikes, and a full list of all goals and dreams, etc. A Role-Playing game at that level might not even use scores or any sort of dice to determine results!
In Roll-Playing gaming, the Character is little more than a collection of scores and derived attributes to be used to chart the "score" a Player has at any one time. In some of these games, names are unimportant, histories are mere flavor text, and the goal is to advance the Characters scores and derived attributes ever onward and upward.
Gygaxian, Arnesonian, and Rein*Hagenian should all be understood; Jacksonian needs a little clarification. Jacksonian refers to both Steve Jackson (the British Jackson, not the American), who wrote the Fighting Fantasy series back in the day; it also refers to Gary Jackson, the fictional creator of the HackMaster game featured in the Knights of the Dinner Table. I should also note that for Dungeons & Dragons purists, you can substitute Hickmanian (Hickmanite?) in place of Rein*Hagenian if you don't want to get vampires mixed in with your dragons...