A cylinder undergoing vertical oscillation penetrates a free surface. The oscillation is controlled to maintain constant maximum acceleration for a range of values of penetration depth. High-image-density particle image velocimetry, which provides instantaneous representations of the vortex development, reveals that several patterns of nearly symmetrical vortices can occur during an oscillation cycle. They originate from distinctive mechanisms of flow separation and vorticity layer development. The key role of the penetration process through the free surface is emphasized by comparison with the corresponding case of the completely submerged cylinder, which generates highly asymmetrical patterns of vortices. An important common feature, however, is the initial formation of a counterflow mixing-layer, corresponding to an elongated layer of vorticity, from the surface of the cylinder. This layer exhibits small-scale Kelvin-Helmholtz vortices and eventually comprises a large-scale vortex.