Surface-enhanced Raman scattering (SERS) signals from molecules adsorbed on the surface of individual clusters of gold nanoparticles are correlated with the structural properties of the nanoparticle clusters. SERS signals were collected from single spherical particles and from clusters composed of two, three, four, or five particles illuminated by 632 nm laser light. The configurations of the individual clusters were characterized by transmission electron microscopy and the intensity of the SERS was found to depend upon both the number and configuration of the particles in each cluster. Average SERS intensities for clusters of like particle number were found to depend nonlinearly upon particle number. Electrodynamic simulations of the near fields of the coupled nanoparticles were performed using the morphological information derived from the electron micrographs. Based upon a generalization of Mie theory that uses particle centered vector spherical harmonics to characterize the fields centered at each particle and vector spherical harmonic addition methods to translate the sphere centered harmonics between particles, the coupled response of each cluster was computed and used to evaluate the field enhancement over the surface of the spheres. The fourth power of the enhanced surface field was calculated for clusters of various configuration and particle number. Averages of simulated SERS enhancement for clusters of like particle number were found to display a dependence upon cluster size that closely matched that of the measured far-field SERS.