  We present optical spectra of SN 2007gr, SN 2007rz, SN 2007uy, SN 2008ax, and
SN 2008bo obtained in the nebular phase when line profiles can lead to
information about the velocity distribution of the exploded cores. We compare
these to 13 other published spectra of stripped-envelope core-collapse
supernovae (Type IIb, Ib, and Ic) to investigate properties of their
double-peaked [O I] 6300, 6364 emission. These 18 supernovae are divided into
two empirical line profile types: (1) profiles showing two conspicuous emission
peaks nearly symmetrically centered on either side of 6300 Angstroms and spaced
approximately 64 Angstroms apart, close to the wavelength separation between
the [O I] 6300, 6364 doublet lines, and (2) profiles showing asymmetric [O I]
line profiles consisting of a pronounced emission peak near 6300 Angstroms plus
one or more blueshifted emission peaks. Examination of these emission profiles,
as well as comparison with profiles in the lines of [O I] 5577, O I 7774, and
Mg I] 4571, leads us to conclude that neither type of [O I] double-peaked
profile is necessarily the signature of emission from front and rear faces of
ejecta arranged in a toroidal disk or elongated shell geometry as previously
suggested. We propose possible alternative interpretations of double-peaked
emission for each profile type, test their feasibility with simple line-fitting
models, and discuss their strengths and weaknesses. The underlying cause of the
observed predominance of blueshifted emission peaks is unclear, but may be due
to internal scattering or dust obscuration of emission from far side ejecta.
