Measurements of branching fractions, rate asymmetries, and angular distributions in the rare decays<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:mi>K</mml:mi><mml:msup><mml:mi>ℓ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>ℓ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:msup><mml:mi>ℓ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>ℓ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>

We present measurements of the flavor-changing neutral current decays B→Kℓ^+ℓ^- and B→K^*ℓ^+ℓ^-, where ℓ^+ℓ^- is either an e^+e^- or μ^+μ^- pair. The data sample comprises 229×10^6 Υ(4S)→BB decays collected with the BABAR detector at the PEP-II e^+e^- storage ring. Flavor-changing neutral current decays are highly suppressed in the standard model and their predicted properties could be significantly modified by new physics at the electroweak scale. We measure the branching fractions B(B→Kℓ^+ℓ^-)=(0.34±0.07±0.02)×10^(-6), B(B→K^*ℓ^+ℓ^-)=(0.78-0.17^(+0.19)±0.11)×10^(-6), the direct CP asymmetries of these decays, and the relative abundances of decays to electrons and muons. For two regions in ℓ^+ℓ^- mass, above and below m_(J/ψ), we measure partial branching fractions and the forward-backward angular asymmetry of the lepton pair. In these same regions we also measure the K^* longitudinal polarization in B→K^*ℓ^+ℓ^- decays. Upper limits are obtained for the lepton-flavor-violating decays B→Keμ and B→K^*eμ. All measurements are consistent with standard model expectations