We report the results of a complete X-ray survey of the Hyades cluster region using the ROSAT All-Sky Survey (RASS). Our survey covers over 900 deg2 of the sky. Over 185 optically identified Hyads were detected down to a limiting X-ray luminosity of ≍1-2 × 1028 ergs s-1 (0.1-1.8 keV); among solar-like stars, i.e., mainsequence stars of spectral type G, the RASS detection rate is ≍90%. The presence of many binary systems in the cluster is a key factor influencing the X-ray luminosity function. Short-period (∼ a few days or less) binaries are anomalously X-ray bright, as might be expected; however, the X-ray luminosity functions of K and possibly M binaries of all types are significantly different from their single counterparts, confirming the results of Pye et al. for a smaller K star sample drawn from deep ROSAT pointings. Comparison with Einstein Observatory studies of a subset of Hyades stars demonstrates a general lack of significant (> a factor of 2) long-term X-ray variability. This may be the result of the dominance of a small-scale, turbulent dynamo in the younger Hyades stars compared to the large-scale, cyclic dynamo observed in the Sun.