In order to assess qualitatively the ejecta geometry of stripped-envelope core-collapse supernovae (SNe), we investigate 98 late-time spectra of 39 objects, many of them previously unpublished. We perform a Gauss-fitting of the O iλλ6300, 6364 feature in all spectra, with the position, full width at half maximum and intensity of the λ6300 Gaussian as free parameters, and the λ6364 Gaussian added appropriately to account for the doublet nature of the O i feature. On the basis of the best-fitting parameters, the objects are organized into morphological classes, and we conclude that at least half of all Type Ib/c SNe must be aspherical. Bipolar jet models do not seem to be universally applicable, as we find too few symmetric double-peaked O i profiles. In some objects, the O i line exhibits a variety of shifted secondary peaks or shoulders, interpreted as blobs of matter ejected at high velocity and possibly accompanied by neutron-star kicks to assure momentum conservation. At phases earlier than ∼200 d, a systematic blueshift of the O iλλ6300, 6364 line centroids can be discerned. Residual opacity provides the most convincing explanation of this phenomenon, photons emitted on the rear side of the SN being scattered or absorbed on their way through the ejecta. Once modified to account for the doublet nature of the oxygen feature, the profile of Mg iλ4571 at sufficiently late phases generally resembles that of O iλλ6300, 6364, suggesting negligible contamination from other lines and confirming that O and Mg are similarly distributed within the ejecta.