By varying the deposition conditions of C-60 thin films and using X-ray diffraction techniques to study the results, we obtain a continuum of structure types ranging from crystalline to amorphous. By measuring the absorption spectra of these films we find that as the film crystallinity increases the fundamental absorption edge and nearby spectral features shift progressively to longer wavelengths. Using a Tauc-type approximation, we find that the optical bandgap E-g=1.3-1.6 eV for crystalline films and E-g=2.4-2.6 eV for amorphous films. Intermediate values of E, are obtained depending upon the degree of crystallinity of the film.