Friction and wear of single layers of graphene have been studied at the micrometer scale. Epitaxial graphene grown by thermal decomposition on SiC-6H(0001) is found to have an initial friction coefficient of 0.02, significantly lower than graphite under the same experimental conditions. During reciprocal sliding the graphene layer is damaged. The evolving friction coefficient of 0.08 for the carbon-rich interface layer terminating the SiC layer is still lower than that of graphite and five times lower than that of the hydrogen-etched SiC substrate. Micrometer-sized patches within the sliding track retain the low friction coefficient of graphene even after hundred sliding cycles.