Single two-dimensional planar silver arrays and one-dimensional linear gold chains of nanoparticles were investigated by dark-field surface plasmon spectroscopy and studied as a function of interparticle distance, particle size, and number of particles. In agreement with recent theoretical predictions, a red shift of the surface plasmon resonance occurring in two-dimensional arrays was found for lattice spacings below 200 nm. This red shift is associated with a significant broadening of the resonance and is attributed to the onset of near-field interactions. We found that the relative contributions of the long-range and short-range interactions in two-dimensional arrays of particles are fundamentally different to those occurring in individual linear chains.