We measured the projected rotational velocities of 1092 northern B stars listed in the Bright Star Catalogue (BSC) and calibrated them against the 1975 Slettebak et al. system. We found that the published values of B dwarfs in the BSC average 27% higher than those standards. Only 0.3% of the stars have rotational velocities in excess of two-thirds of the breakup velocities, and the mean velocity is only 25% of breakup, implying that impending breakup is not a significant factor in reducing rotational velocities. For the B8-B9.5 III-V stars the bimodal distribution inV can be explained by a set of slowly rotating Ap stars and a set of rapidly rotating normal stars. For the B0-B5 III-V stars that include very few peculiar stars, the distributions inV are not bimodal. Are the low rotational velocities of B stars due to the occurrence of frequent low-mass companions, planets, or disks? The rotational velocities of giants originating from late B dwarfs are consistent with their conservation of angular momentum in shells. However, we are puzzled by why the giants that originate from the early B dwarfs, despite having 3 times greater radii, have nearly the same rotational velocities. We find that all B-type primaries in binaries with periods less than 2.4 days have synchronized rotational and orbital motions; those with periods between 2.4 and 5.0 days are rotating within a factor 2 of synchronization or are "nearly synchronized." The corresponding period ranges for A-type stars are 4.9 and 10.5 days, or twice as large. We found that the rotational velocities of the primaries are synchronized earlier than their orbits are circularized. The maximum orbital period for circularized B binaries is 1.5 days and for A binaries is 2.5 days. For stars of various ages from 10^7.5 to 10^10.2 yr the maximum circularized periods are a smooth exponential function of age.