I've been thinking about this as well lately. The role that Arthur fills in this movie is best described using a term from a fave show of mine, "Hustle". Arthur is the Fixer. Everyone else comes up with the grand schemes and plans, but Arthur is the one to makes shit happen. He's the planner in the logical, real world, where Eames and Cobb and Ariadne are the planners in the more imaginative "think outside the box" kind of way. Not that Arthur lacks imagination (as the elevator kick proves) just that he is more apt to think in real world, physical, logical terms, not emotional, more ephemeral ones.

One thing that I've noticed upon watching this movie (over and over and over again) is that everyone has a definitive job that they fill in the real world. As in, if there were no such thing as dream sharing, they are already doing something they would do. Ariadne and Cobb are architects, Eames is a grifter (con man), and Yusuf is a chemist. But Arthur doesn't have definition without the dream world.

I think that's why so much of Arthur's characterization is fanon. After all, really all we're given on Arthur is that he's known Cobb a long time, has been friends with him since a good time before Mal's death, he's the one in charge of researching the marks, and knows Eames before the movie, but doesn't get along well with him. We know that Cobb turned to extraction after Mal died, but we don't know how Arthur got roped into it (loyalty to a friend? his idea in the first place? already was a thief type?) and outside of being "a stick in the mud" we aren't even really given much personality.

We writers really have to extrapolate and try to build in personality traits and thought patterns that fill in the holes that are left. We're drawn in by the little pieces that JGL's acting gives us ("the kiss" was -not- part of the shooting script), and by the general smooth, dapper look that Arthur gives, but it's mostly just that he's hot and we want to write stories with him in it. :P