In this paper, I review some of the basic properties of the pulsar population in globular clusters (GCs) and compare it with the the Galactic disk population. The neutron stars (NSs) in GCs were likely formed - and appear to continue forming - in highly symmetric supernovae (SNe), likely from accretion-induced collapse (AIC). I review the many pulsar finds and discuss some particularly well populated GCs and why they are so. I then discuss some particularly interesting objects, like millisecond pulsars (MSPs) with eccentric orbits, which were heavily perturbed by passing stars. Some of these systems, like NGC 1851A and NGC 6544B, are almost certainly the result of exchange interactions, i.e., they are witnesses to the very same processes that created the large population of MSPs in the first place. I also review briefly the problem posed by the presence of young pulsars in GCs (with a special emphasis on a sub-class of young pulsars, the super-energetic MSPs), which suggest continuing formation of NSs in low-velocity SNe. In the final section, I discuss the possibility of an analogous population in the Galaxy and highlight a particularly interesting case, PSR J1903+0327, where the primary neutron star appears to have formed with a small-velocity kick and small fractional mass loss. Systems with primary NSs formed in electron-capture SNe should constitute a distinct low-velocity Galactic population akin in many respects to the GC population. Current high-resolution surveys of the Galactic plane should be able to detect it clearly.