We report measurements of the electronic structure and surface morphology of exfoliated graphene on an insulating substrate using angle-resolved photoemission and low energy electron diffraction. Our results show that although exfoliated graphene is microscopically corrugated, the valence band retains a massless fermionic dispersion, with a Fermi velocity of ~10^6 m/s. We observe a close relationship between the morphology and electronic structure, which suggests that controlling the interaction between graphene and the supporting substrate is essential for graphene device applications.