We have used multiband high-resolution HST WFPC2 and ACS observations combined with wide-field ground-based observations to study the blue straggler star (BSS) population in the Galactic globular cluster NGC 6388. As in several other clusters we have studied, the BSS distribution is found to be bimodal: highly peaked in the cluster center, rapidly decreasing at intermediate radii, and rising again at larger radii. In other clusters the sparsely populated intermediate-radius region (or ``zone of avoidance'') corresponds well to that part of the cluster where dynamical friction would have caused the more massive BSSs or their binary progenitors to settle to the cluster center. Instead, in NGC 6388, BSSs still populate a region that should have been cleaned out by dynamical friction effects, thus suggesting that dynamical friction is somehow less efficient than expected. As a by-product of these observations, the peculiar morphology of the horizontal branch (HB) is also confirmed. In particular, within the (very extended) blue portion of the HB we are able to clearly characterize three subpopulations: ordinary blue HB stars, extreme HB stars, and blue hook stars. Each of these populations has a radial distribution which is indistinguishable from normal cluster stars. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555. Also based on Wide Field Imager observations collected at the European Southern Observatory, La Silla, Chile.