Rare charmless hadronic B decays are particularly interesting because of their importance in understanding the CP violation, which is essential to explain the matter-antimatter asymmetry in our universe, and of their roles in testing the ''effective'' theory of B physics. The study has been done with the BABAR experiment, which is mainly designed for the study of CP violation in the decays of neutral B mesons, and secondarily for rare processes that become accessible with the high luminosity of the PEP-II B Factory. In a sample of 89 million produced B{bar B} pairs on the BABAR experiment, we observed the decays B{sup 0} {yields} {omega}K{sup 0} and B{sup +} {yields} {omega}{rho}{sup +} for the first time, made more precise measurements for B{sup +} {yields} {omega}h{sup +} and reported tighter upper limits for B {yields} {omega}K* and B{sup 0} {yields} {omega}{rho}{sup 0}.