Poisson's ratio, the relation between lateral contraction of a thin, linearly elastic rod when subjected to a longitudinal extension, has a long and interesting history. For isotropic bodies, it can theoretically range from +1/2 to -1; the experimental gamut for anisotropics is even larger. The ratio is positive for all combinations of directions in most crystals. But as far back as the 1800s, Voigt and others found that negative values were encountered for some materials, a property now called auxeticity. Here we examine this property from the point of view of crystal stability and compute extrema of the ratio for various interesting and technologically important materials. Potential applications of the auxetic property are mentioned.