The rare decays B-0 -> K-*0 mu(+)mu(-) and B-s -> phi mu(+)mu(-) are now being observed with enough precision to test Standard Model predictions. A full understanding of these decays requires accurate determinations of the corresponding hadronic form factors. Here we present results of lattice QCD calculations of the B -> K-* and B-s -> phi form factors. We also determine the form factors relevant for the decays B-s -> K*l nu and B-s -> (K) over bar (*0)l(+)l(-). We use full-QCD configurations including 2 + 1 flavors of sea quarks using an improved staggered action, and we employ lattice nonrelativistic QCD to describe the bottom quark.