American Heritage Dictionary: "A tersely phrased statement of a truth or opinion. A brief statement of a principle."
Hutchinson Encyclopaedia: "Short, sharp, witty saying, usually making a general observation"
Oxford Literary Dictionary: a statement of some general principle, expressed memorably by condensing much wisdom into few words.
Columbia Encyclopedia: "short, pithy statement of an evident truth concerned with life or nature. ... Hippocrates was the first to use the term for his 'Aphorisms', [a book of] briefly stated medical principles."
Encarta Dictionary Etymology: Early 16th century, derived from: French aphorisme, derived from: Greek aphorizein "define", derived from: Greek horizein "delimit" (see horizon - place where earth meets sky; the range or limits of somebody's interests, knowledge, or experience)
Online Etymology Dictionary: from Gk. aphorismos "definition, pithy sentence," from aphorizein "to mark off, divide" apo- "from" + horizein "to bound."
Wikipedia 7/2007: "an aphorism is a saying that makes a point or expresses the opinion of the speaker by illustrating or describing the horizon of that perspective. Instead of standing outside a viewpoint and describing the viewpoint, an aphorism adopts a viewpoint and identifies the things which are only visible from that perspective.
Nietzsche: Whoever writes in blood and aphorisms does not want to be read but to be learned by heart. In the mountains the shortest way is from peak to peak: but for that one must have long legs. Aphorisms should be peaks - and those who are addressed, tall and lofty. (Zarathustra 'On Reading and Writing'). The aphorism, the maxim ... are the forms of 'eternity'; it is my ambition to say in ten sentences what everyone else says in a book - what everyone else does not say in a book. (Twilight of the Idols, part 8, sect 51)
My view of aphorisms can be seen in paragraph 5 of the page Luccaph Characteristics.