From a simple time-dependent tight-binding model, we calculate the absorption spectra of a series of metallic nanoparticles of varying size and shape. Spheres and spheroids of varying aspect ratios as well as a number of polyhedral particle shapes are studied. The frequency of the maximum absorption is found to scale linearly with the surface to volume ratio of the particle with a slope and intercept, which depends on particle shape, in particular, on the deviation from sphericity. In the case of spheroids, the shifts of the two different plasmon peaks that are observed are characterized as a function of the aspect ratio. The influence of shape is seen to be a determining factor for the frequency of the plasmon resonance. The influence of adatoms is studied. Linear relations between surface adatom concentration and the width of the spectral feature as well as the peak energy are observed.