The Age of the Essay describes what an essay actually is - and it's not the introduction-three-paragraphs-conclusion thing that everybody hates to write.
Actually, because I thought it was so good, I linked to it in the "writer's guidelines" for this site. :-)
The point that stuck with me from his essay is that "one learns nothing from what one expects." If you take an essay as a "try" and do some exploring on a subject, you may learn something. And if you learn something, chances are your readers will too. Sometimes it won't necessarily be a fact that you learn, but several facts that you already knew made a surprising connection. For example, I knew that "essay" was from "essai" which means "try", but I didn't know how that connected to the essays we all had to write in high school. Now I do - we weren't writing real essays in high school. We were writing short dissertations - defences of a thesis statement.
An essay as Graham describes it is, I think, the kind of thing I would love to see more of on this site. Pick a subject and explore it, make links you hadn't thought of before, find a couple of facts you weren't aware of - then present that to everybody else. It sounds to me like much more fun to write - and read. It also reduces the need for the writer to be an authority. In a field where the "authorities" all say contradictory things, I think an exploration is more valuable than a flat statement of personal preference disguised as a rule.
Although as I mentioned, I find Graham's essays rather rambling - he could probably stand some editing once the first "try" is written to make it more concise (and more appealing for busy surfers to read). The order thoughts present themselves to the writer may show a bit about how the writer thinks, but aren't always in the order best suited for reading.