We report the discovery of three binary millisecond pulsars in circular orbits with low-mass companions from a continuing survey of the southern sky with the Parkes radio telescope. The three pulsars, PSR J0034-0534, PSR J1045-4509, and PSR J2145-0750 have pulse periods of 1.87, 7.47, and 16.05 ms and orbital periods of 1.6, 4.1, and 6.8 days, respectively. PSR J2145-0750 has a spin-down age of approximately greater than 12 Gyr, which raises interesting questions about its progenitor and initial pulse period. The properties of the growing class of radio pulsars with low-mass companions are discussed, and we suggest that their velocities, and a tendency for the short-period pulsars to have small orbital periods, are consistent with their formation from Type II supernova explosions....