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We derive the atomic hydrogen content for a total of 1900 spirals in the fields of 18 nearby clusters. By comparing the H I-deficiency distributions of the galaxies inside and outside one Abell radius (RA) of each cluster, we find that two-thirds of the clusters in our sample show a dearth of neutral gas in their interiors. Possible connections between the gaseous deficiency and the characteristics of both the underlying galaxies and their environment are investigated in order to gain insight into the mechanisms responsible for H Idepletion. While we do not find a statistically significant variation of the fraction of H I-deficient spirals in a cluster with its global properties, a number of correlations emerge that argue in favor of the interplay between spiral disks and their environment. In the clusters in which neutral gas deficiency is pronounced, we see clear indications that the degree of H Idepletion is related to the morphology of the galaxies and not to their optical size; early-type and probably dwarf spirals are more easily emptied of gas than the intermediate Sbc-Sc types. Gas contents below 1/10, and even 1/100, of the expectation value have been measured, implying that gas removal is very efficient. The radial extent of the region with significant gas ablation can reach up to 2RA. Within this zone, the proportion of gas-poor spirals increases continuously toward the cluster center. The wealth of 21 cm data collected for the Virgo region has made it possible to study the two-dimensional pattern of H Ideficiency in that cluster. The map of gas deficiency in the Virgo central area points to an scenario in which gas losses result from the interaction of the disks with the inner hot intracluster gas around M87. We also find evidence that gas-poor spirals in H I-deficient clusters move in orbits more radial than those of the gas-rich objects. The implications of all these results on models of how galaxies interact with their environment are reviewed. Hydrodynamic effects appear as the most plausible cause of H Iremoval.