We present scanning tunneling microscopy (STM) images of single-layer graphene crystals examined under ultrahigh vacuum conditions. The samples, with lateral dimensions on the micrometer scale, were prepared on a silicon dioxide surface by direct exfoliation of crystalline graphite. The single-layer films were identified by using Raman spectroscopy. Topographic images of single-layer samples display the honeycomb structure expected for the full hexagonal symmetry of an isolated graphene monolayer. The absence of observable defects in the STM images is indicative of the high quality of these films. Crystals composed of a few layers of graphene also were examined. They exhibited dramatically different STM topography, displaying the reduced threefold symmetry characteristic of the surface of bulk graphite.