We systematically search for discrete absorption events in the vast archive of the Rossi X-ray Timing Explorer. This includes dozens of nearby type I and Compton-thin type II AGN and covers timescales from days to over a decade for individual objects. We are sensitive to discrete absorption events due to clouds of full-covering, neutral or mildly-ionized gas with columns 1022−25 cm−2 transiting the line of sight. We detect 13 eclipse events in 8 objects, roughly tripling the number of previously published events from this archive. Despite sensitivity to events with NH up to 1024−25 cm−2, we measured no Compton-thick eclipses in our sample. Peak column densities span 2.5–19 × 1022 cm−2. Event durations span hours to months. We infer the clouds distances from the black hole, assuming Keplerian motion, to span 0.2–80 × 104 Schwarzschild radii. We find no statistically significant difference between the individual cloud properties of type I and II objects. The presence of eclipses in both type Is and IIs argues against sharp-edged cloud distributions. The type II AGN show a level of “base-line” X-ray absorption that is consistent with being constant over timescales from 0.6 to 8.4 yr. This can either be explained by a homogeneous medium, or by X-ray-absorbing clouds that each have NH ≪ 1022 cm−2. Considering the “selection function” of the monitoring, we derive the probability of cloud occultation events. Finally, we derive the first X-ray statistical constraints for clumpy-torus models.