Using high-resolution reflection electron-energy-loss spectroscopy (HREELS), we compare experimental results for the wave-vector-dependent behavior of plasmons in a graphene sheet on SiC(0001) with that due to a filled band of surface states on semiconducting silicon. There are significant differences in behavior between the two systems and the behavior predicted for a classical two-dimensional sheet of electrons. In particular, the damping increases with wave vector independent of any obvious inelastic scattering channel. The results illustrate the importance of finite-momentum, nonlocal potential effects for the dynamical behavior of electrically isolated charge sheets.