The 5x5,6 root 3x6 root 3-R30 degrees and graphene-covered 6 root 3x6 root 3-R30 degrees reconstructions of the SiC(0001) surface are studied by scanning tunneling microscopy and spectroscopy. For the 5x5 structure a rich spectrum of surface states is obtained, with one state, in particular, found to be localized on top of structural protrusions (adatoms) observed on the surface. Similar spectra are observed on the bare 6 root 3x6 root 3-R30 degrees reconstruction, and in both cases the spectra display nearly zero conductivity at the Fermi level. When graphene covers the 6 root 3x6 root 3-R30 degrees surface the conductivity at the Fermi level shows a marked increase, and additionally the various surface state peaks seen in the spectrum shift in energy and fall in intensity. The influence of the overlying graphene on the electronic properties of the interface is discussed, as are possible models for the interface structure.