Context. O stars are excellent tracers of the intervening ISM because of their high luminosity, blue intrinsic SED, and relatively featureless spectra. We are currently conducting the Galactic O-Star Spectroscopic Survey (GOSSS), which is generating a large sample of O stars with accurate spectral types within several kpc of the Sun. Aims. We aim to obtain a global picture of the properties of dust extinction in the solar neighborhood based on optical-NIR photometry of O stars with accurate spectral types. Methods. We have processed a carefully selected photometric set with the CHORIZOS code to measure the amount [E(4405 − 5495)] and type [R 5495 ] of extinction towards 562 O-type stellar systems. We have tested three different families of extinction laws and analyzed our results with the help of additional archival data. Results. The Maíz Apellániz et al. (2014, A&A 564, A63) family of extinction laws provides a better description of Galactic dust that either the Cardelli et al. , ApJ 345, 245) or Fitzpatrick (1999 families, so it should be preferentially used when analyzing samples similar to the one in this paper. In many cases O stars and late-type stars experience similar amounts of extinction at similar distances but some O stars are located close to the molecular clouds left over from their births and have larger extinctions than the average for nearby late-type populations. In qualitative terms, O stars experience a more diverse extinction than late-type stars, as some are affected by the small-grain-size, low-R 5495 effect of molecular clouds and others by the large-grain-size, high-R 5495 effect of H ii regions. Late-type stars experience a narrower range of grain sizes or R 5495 , as their extinction is predominantly caused by the average, diffuse ISM. We propose that the reason for the existence of large-grain-size, high-R 5495 regions in the ISM in the form of H ii regions and hot-gas bubbles is the selective destruction of small dust grains by EUV photons and possibly by thermal sputtering by atoms or ions.