We measured the cross section and response functions for the quasielastic 16O(e,e'p) reaction for missing energies 25< or =E(m)< or =120 MeV at missing momenta P(m)< or =340 MeV/c. For 25<E(m)<50 MeV and P(m) approximately 60 MeV/c, the reaction is dominated by a single 1s(1/2) proton knockout. At larger P(m), the single-particle aspects are increasingly masked by more complicated processes. Calculations which include pion exchange currents, isobar currents, and short-range correlations account for the shape and the transversity, but for only half of the magnitude of the measured cross section.