Angular distributions for the elastic scattering of {sup 8}B, {sup 7}Be, and {sup 6}Li on a {sup 12}C target have been measured at E{sub lab}=25.8, 18.8, and 12.3 MeV, respectively. The analyses of these angular distributions have been performed in terms of the optical model using Woods-Saxon and double-folding type potentials. The effect of breakup in the elastic scattering of {sup 8}B+{sup 12}C is investigated by performing coupled-channels calculations with the continuum discretized coupled-channel method and cluster-model folding potentials. Total reaction cross sections were deduced from the elastic-scattering analysis and compared with published data on elastic scattering of other weakly and tightly bound projectiles on {sup 12}C, as a function of energy. With the exception of {sup 4}He and {sup 16}O, the data can be described using a universal function for the reduced cross sections.