Context. The spectroscopic characterization of many O-type stars is hampered by a nearby companion. Aims. We want to obtain spatially resolved spectroscopy of close O-type visual binaries to derive their spectral types. Methods. We used the Space Telescope Imaging Spectrograph (STIS) of the Hubble Space Telescope (HST) to obtain long-slit blue-violet spectroscopy of eight Galactic O-type stars with nearby visual companions and used spatial-profile fitting to extract the separate spectra. We also used the ground-based Galactic O-Star Spectroscopic Survey to study more distant visual components. Results. We spatially resolve seven of the eight systems, present spectra for their components, and obtain their spectral types. Those seven multiple systems are ι Ori Aa,Ab,B; 15 Mon Aa,Ab,C; τ CMa Aa,Ab,B,C,D,E; HD 206 267 Aa,Ab,C,D; HD 193 443 A,B; HD 16 429 Aa,Ab; and IU Aur A,B. This is the first time that spatially resolved spectroscopy of the close visual binaries of those systems is obtained. We establish the applicability of the technique as a function of the separation and magnitude difference of the binary.