A recently developed method for deriving anisotropic atomic dipole polarizability tensors has been employed to derive these terms for each of the atoms in seven families of organic compounds: alcohols, alkanes, amides, amines, carboxylic acids, sulfur compounds, and benzene rings. The procedure uses fits to ab initio quantum mechanically computed molecular polarizability data to determine effective atomic polarizability tensor parameters. A new representation is described which uses bond increments, a property of the bonds rather than simply the atomic types, for polarizability components both parallel and perpendicular to the bonds. It is shown to give excellent results as gauged by its reproduction of the exact ab initio polarizabilities. We examine the accuracy of the ab initio isotropic polarizabilities compared to experiment and present a simple scaling procedure for the former. The isotropic approximations to the full anisotropic atomic polarizabilities are compared for differing atom types and bonding environments. The resulting molecular isotropic polarizabilities are also compared where possible with experiment. The present model consistently predicts both experimental isotropic molecular polarizabilities and empirically derived atomic parametrizations precisely within a few percent.