Core-collapse supernovae (CC-SNe) are the explosions that announce the death of massive stars. Some CC-SNe are linked to long-duration gamma-ray bursts (GRBs) and are highly aspherical. One important question is to what extent asphericity is common to all CC-SNe. Here we present late-time spectra for a number of CC-SNe from stripped-envelope stars and use them to explore any asphericity generated in the inner part of the exploding star, near the site of collapse. A range of oxygen emission-line profiles is observed, including a high incidence of double-peaked profiles, a distinct signature of an aspherical explosion. Our results suggest that all CC-SNe from stripped-envelope stars are aspherical explosions and that SNe accompanied by GRBs exhibit the highest degree of asphericity.