Scanning tunneling microscopy (STM) has been use to obtain images and current-voltage (I-V)curves of carbon nanotubes produced by arc discharge of carbon electrodes. The STM I- V curves indicate that carbon nanotubes with diameters from 2.0 to 5.1 nm have a metallic density of states. Using STM, we also observe nanometer-size graphene sheets which are four graphite layers thick. The STM images of carbon nanotubes are in good agreement with transmission electron microscope images.