  [ABRIDGED] 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 GOSSS, which is generating a
large sample of O stars with accurate spectral types within several kpc of the
Sun. Aims. 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 photometric set with the CHORIZOS
code to measure the amount and type 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
Ma\'iz Apell\'aniz et al. (2014) family of extinction laws provides a better
description of Galactic dust that either the Cardelli et al. (1989) or
Fitzpatrick (1999) families, so it should be preferentially used. 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.
