James Mishler of Adventures in Gaming has created a cool alignment graph of game styles here.
I am firmly wedged on the Arneson-Roleplaying axis. Neither tending towards High Adventure or Story-Teller. The reason for this is that while I run my campaign sandbox-style, role-playing and immersion are very important to my campaigns. The immersion tends to make my games more focused than a free range, anything goes style campaign focused on adventure.
Stuart asks a good questions "What is the difference between Arnesonian and Jacksonian"
Roll-play versus Roleplaying. It not so much an attitude towards the mechanics. I am a true Grognard myself. It is more an attitude to character development.
To some people the character is no more personal than a plastic piece in a monopoly game. Their "roleplaying" is primarily themselves interacting with the setting.
The polar opposite is the person who creates a background for their character and immerses themselves not only into the mechanics of the game but the personality of the character. Similar to what a good actor does
(like Karl Urban as Doctor McCoy in the new Star Trek vs Tom Cruise in... well just about anything he does)
As a GM, I long stopped worrying about these opposite styles. Where me being Neutral Arneson comes into play is that my games is that pure Jacksonian player need to think about the long-term consequences of his actions and not just whatever works to achieve his immediate goals. So things like flaming the guards and burning the village tend to cause the character to wind up as a donkey offering rides to whoever approaches the city gates.
On the flip side I tend to like to referee RPGs with tactically rich combat rules. So I guess that means that I am not wedged up on the high end of the Arneson but perhaps a 1/3 or 2/3 of the way towards true neutral.