Molecular static and dynamic polarizabilities for thirteen small molecules have been calculated using four "black box" ab initio methods, the random phase approximation, RPA, the second-order polarization propagator approximation, SOPPA, the second-order polarization propagator approximation with coupled cluster singles and doubles amplitudes, SOPPA(CCSD), and the coupled cluster singles and doubles linear response function method, CCSDLR. The frequency dependence of the polarizabilities is given in terms of the dipole oscillator strength sum rules or Cauchy moments S(-4) and S(-6). Two basis sets were employed, Sadlej's medium size polarized basis set and Dunning's correlation consistent basis set of triple- quality augmented by two diffuse functions of each angular momentum (daug-cc-pVTZ). The results are compared to other theoretical results as well as to experimental values for the static polarizabilities, polarizability anisotropies, and Cauchy moments. Frequency-dependent polarizabilities and polarizability anisotropies, calculated at the CCSDLR level using the daug-cc-pVTZ basis set, are presented for five typical laser frequencies.