Graphene-derived nanomaterials are emerging as ideal candidates for postsilicon electronics. Elucidating the electronic interaction between an insulating substrate and few-layer graphene (FLG) films is crucial for device applications. Here, we report electrostatic force microscopy (EFM) measurements revealing that the FLG surface potential increases with film thickness, approaching a "bulk" value for samples with five or more graphene layers. This behavior is in sharp contrast with that expected for conventional conducting or semiconducting films, and derives from unique aspects of charge screening by graphene's relativistic low energy carriers. EFM measurements resolve previously unseen electronic perturbations extended along crystallographic directions of structurally disordered FLGs, likely resulting from long-range atomic defects. These results have important implications for graphene nanoelectronics and provide a powerful framework by which key properties can be further investigated.