We present some recent measurements of rare flavor-changing neutral current B decays, using
data collected with the BABAR detector at the PEP-II e+e− collider at SLAC. First, we search for the rare process B+ → K+τ+τ− and we do not find evidence for a signal. The measured branching fraction is (1.31+0.66-0.61(stat.)+0.35-0.25(sys.)) × 10−3 with an upper limit, at the 90% confidence level, of B(B → K+τ+τ−) < 2.25 × 10−3. We then study the lepton forward-backward asymmetry AFB and the longitudinal K∗ polarization FL in the rare decays B → K∗l+l−, where l+l− is either e+e− or μ+μ−. We report results for both the K∗(892)0l+l− and K∗(892)+l+l− final states, as well as their combination K∗l+l−, in five disjoint dilepton mass-squared bins. Finally, we measure the time-dependent CP asymmetry in the radiative-penguin decay B0 → KS0π−π+γ. The Kππ resonant structure is extracted by an amplitude analysis of the mKππ and mKπ spectra in B+ → K+π−π+γ decays. We use these results to extract the mixing-induced CP parameters of the process B0 → KS0ρ0γ from the time-dependent analysis of B0 → KS0π+π−γ decays and obtain S = −0.18 ± 0.32(stat.)+0.06 (syst.).