We present observations of 136 RS CVn active binary systems obtained with the ROSA T Position Sensitive Proportional Counter (PSPC) during the All-Sky Survey phase of the mission. Of this sample, 112 targets were detected in exposures of approximately 600 s or less. This represents the largest sample of RS CVn systems observed to date at any wavelength, including X-rays. Furthermore, since the entire sky was surveyed, these data do not suffer from any biases other than those present in the methods used to discover the RS CVn binaries. A maximum value of F(X)/F(bol) approximately 10(-3), where F(X) is the surface flux, is found with no apparent dependence on (B - V) color. This is consistent with the hypothesis that there is a maximum (''saturated'') coronal heating rate for the most active and rapidly rotating stars. No correlation between L(X) and L(bol) is evident in the data. We observe a decrease in surface flux with increasing period for the entire sample, but this trend results from the giants and subgiants since for dwarfs the surface fluxes are independent of rotation period. For the evolved stars, the flux-period relation results from the strong correlation of period and stellar radius. No dependence of X-ray emission on v(rot), orbital separation or the Roche lobe filling fraction is observed. We demonstrate that the secondary does not affect the activity level of the system other than inducing, and maintaining, rapid rotation in the active star. Except for dwarfs, the rotation period provides the best stellar or orbital parameter to predict the X-ray surface flux level. Comparison of the X-ray properties of the RS CVn systems with 6 cm radio and C iv ultraviolet emission is also presented.