We report on the fabrication and measurement of devices designed to study the electrochemical behavior of individual monolayer graphene sheets as electrodes. We have examined both mechanically exfoliated and chemical vapor deposited (CVD) graphene. The effective device areas, determined from cyclic voltammetric measurements, show good agreement with the geometric area of the graphene sheets, indicating that the redox reactions occur on clean graphene surfaces. The electron transfer rates of ferrocenemethanol at both types of graphene electrodes were found to be more than 10-fold faster than at the basal plane of bulk graphite, which we ascribe to corrugations in the graphene sheets. We further describe an electrochemical investigation of adsorptive phenomena on graphene surfaces. Our results show that electrochemistry can provide a powerful means of investigating the interactions between molecules and the surfaces of graphene sheets as electrodes.