High energy neutrino astronomy opens a window on the universe that is not accessible with photons, offering an opportunity to obtain information about both astrophysical sources and fundamental particle physics. Neutrino telescopes, such as IceCube, will have the ability to measure both the energy spectrum and flavor content of high energy neutrino fluxes. Flavor ratios can be determined by comparing the rate of shower events to muon tracks, with additional information provided by the observation of tau lepton “lollipop” or “double-bang” events. The peak sensitivities of these interactions occur at different energies, but the flavor ratios can be reliably constructed if a reasonable measurement is made of the spectrum shape. Various exotic neutrino properties may be revealed by such flavor ratio measurements, for example, neutrino decay (for which existing limits are extremely weak) can result in extreme deviations to the expected flavor ratios. In addition, the enormous path-length of astrophysical neutrino experiments allows a sensitivity to extremely small neutrino mass-squared differences. This can be used to probe possible pseudo-Dirac splittings of each generation, and thus reveal Majorana mass terms (and lepton number violation) not discernible via any other means.