We report the observation of the b -> d penguin-dominated decay B-0 -> K-*0(K) over bar (*0) with a sample of 383.2 +/- 4.2 million B (B) over bar pairs collected with the BABAR detector at the PEP-II asymmetric-energy e(+)e(-) collider at the Stanford Linear Accelerator Center. The measured branching fraction is B(B-0 -> K-*0(K) over bar (*0))=[1.28(-0.30)(+0.35)+/- 0.11]x10(-6) and the fraction of longitudinal polarization is f(L)(B-0 -> K-*0(K) over bar (*0))=0.80(-0.12)(+0.10)+/- 0.06. The first error quoted is statistical and the second systematic. We also obtain an upper limit at the 90% confidence level on the branching fraction for B(B-0 ->(KK*0)-K-*0)< 0.41x10(-6).