Grapher: A program for drawing graphs.
First, please allow a small explanation: What a mathematician might call a "graph" is likely to be different than what a preppy, yuppie, or bobo1 might call a graph. It is a collection of things (nodes), for which each pair of things is either connected or not. What matters is not what the things represent nor whether or not the things have mass or loci in space, but the aggregate pattern (in a non-geometric sense) of the connections between those things. What a non-mathematician might call a graph might more preferably be called a "chart", or a "plot", or an "informal illustration used to persuade" by a mathematician. This link explains a bit more about graph theory.
The Grapher program (it has had this name ever since it was first hatched on an Andrew workstation at Carnegie Mellon in 1987 or 1988) allows someone to draw, edit and investigate a graph.
Grapher is written in JavaScript, which means that a large number of programmers can, in theory, contribute to its development (because of the web, more people program in JavaScript than probably any other language). It has a graphical user interface, largely patterned after the Windows/Macintosh GUI. It reads and writes XML formatted data (generally consistent with GraphML, though preferring a sparse data format for edges). It is copyrighted, but open-source. Alas, because of the way it draws lines to the screen (Microsoft VML), it only works in Internet Explorer (4.0 or higher). It doesn't currently work in the Netscape web browser.
1. "Bobos": bourgeois bohemians (from the book, Bobos in Paradise: The New Upper Class and How They Got There, by David Brooks, New York: Simon and Schuster, 2000).
2. A crossover graph (for showing that three-coloring of planar graphs is NP-complete) from "Crossover graphs and generalized input/output coloring problems in the plane" David Dailey, in Journal of Combinatorics, Information and Systems Sciences, 1980, 5:271-280.
3. Elephant head taken from Images in the Public Domain, originally from Webster's New International Dictionary of the English Language, 1911, G & C Merriam Co. Springfield, MA.