The formation of epitaxial graphene on SiC(0001) surfaces is studied using atomic force microscopy, Auger electron spectroscopy, electron diffraction, Raman spectroscopy, and electrical measurements. Starting from hydrogen-annealed surfaces, graphene formation by vacuum annealing is observed to begin at about 1150°C, with the overall step-terrace arrangement of the surface being preserved but with significant roughness (pit formation) on the terraces. At higher temperatures near 1250°C, the step morphology changes, with the terraces becoming more compact. At 1350°C and above, the surface morphology changes into relatively large flat terraces separated by step bunches. Features believed to arise from grain boundaries in the graphene are resolved on the terraces, as are fainter features attributed to atoms at the buried graphene/SiC interface.