Few-nucleon transfer reactions have been measured for the systems {sup 64}Ni+{sup 208}Pb and {sup 80}Se+{sup 208}Pb at energies slightly above the Coulomb barrier. Together with previous data, heavy-ion-induced transfer reactions on {sup 208}Pb have now been studied with projectiles in the mass range {ital A}=12--86. The experimental total reaction cross sections and the yields for quasielastic processes are compared with various theoretical predictions. For the one- and two-nucleon transfer reactions a systematic behavior of the energy- and angle-integrated cross sections is observed. This behavior can be understood within a simple semiclassical model. A comparison of the cross-section ratios between one- and two-neutron and the one- and the two-proton transfer reactions indicates that the two-proton-transfer process shows an enhancement with respect to the one-proton transfer reaction.