The recent application of tunneling probes in electronic structure studies of carbon nanotubes has proven both powerful and challenging. Using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS), local electronic properties in ordered aggregates of carbon nanotubes (multiwalled nanotubes and ropes of single walled nanotubes) have been probed. In this report, we present evidence for interlayer (concentric tube) interactions in multiwalled tubes and tube-tube interactions in singlewalled nanotube ropes. The spatially resolved, local electronic structure, as determined by the local density of electronic states, is shown to clearly reflect tube-tube interactions in both of these aggregate forms.