Hipparcos trigonometric parallaxes are used to estimate the distances to the maximum possible number of open star clusters (OSC); distance moduli are estimated for 45 clusters with maximum heliocentric distances of about 1000 pc. The latter value can serve as an estimate of the limit to which it still makes sense to use Hipparcos trigonometric parallaxes to determine the distances to small groups composed of 6–10 sufficiently bright stars. A systematic correction to the distance moduli of clusters from the homogeneous catalog of OSC parameters (Loktin et al. 1997, 2000) is estimated, which turns out to be independent of the cluster age.