Recent surveys of Galactic globular clusters have been very effective at discovering radio pulsars. By a careful analysis of selection effects in the various surveys, and after estimating the relative efficiency of pulsar production in the individual clusters, we obtain a census of the cluster population of pulsars. We find that there are ∼104 pulsars in the Galactic globular clusters, subject to uncertainties in pulsar beaming and binarity. Such a large population poses severe problems for the standard model of pulsar production in clusters, unless the uncertain factors due to beaming and binarity are pushed to values inconsistent with our present expectations. This suggests the need for a substantial modification of the standard model, either by including accretion-induced collapse of massive white dwarfs or by increasing the retention of primordial neutron stars in the clusters. We also find that the birthrate of pulsars exceeds that of their presumed progenitors, the cluster low-mass X-ray binaries, by a large factor. This discrepancy, and a similar discrepancy for the binary and millisecond pulsars in the Galactic disk, can be resolved if the X-ray lifetime of low-mass X-ray binaries is ∼100 times shorter than generally assumed. Finally, we present a table of the estimated numbers of pulsars in the rich globular clusters visible from the northern hemisphere. This table should be of interest to observers involved in pulsar searches.