  Most Type I superluminous supernovae (SLSNe-I) reported to date have been
identified by their high peak luminosities and spectra lacking obvious signs of
hydrogen. We demonstrate that these events can be distinguished from
normal-luminosity SNe (including Type Ic events) solely from their spectra over
a wide range of light-curve phases. We use this distinction to select 19
SLSNe-I and 4 possible SLSNe-I from the Palomar Transient Factory archive
(including 7 previously published objects). We present 127 new spectra of these
objects and combine these with 39 previously published spectra, and we use
these to discuss the average spectral properties of SLSNe-I at different
spectral phases. We find that Mn II most probably contributes to the
ultraviolet spectral features after maximum light, and we give a detailed study
of the O II features that often characterize the early-time optical spectra of
SLSNe-I. We discuss the velocity distribution of O II, finding that for some
SLSNe-I this can be confined to a narrow range compared to relatively large
systematic velocity shifts. Mg II and Fe II favor higher velocities than O II
and C II, and we briefly discuss how this may constrain power-source models. We
tentatively group objects by how well they match either SN 2011ke or PTF12dam
and discuss the possibility that physically distinct events may have been
previously grouped together under the SLSN-I label.
