| We have searched a sample of 9.6 M BB¯ events collected with the CLEO II detector in e+e - annihilations at the Upsilon(4S) resonance for B meson decays as follows: (1) The flavor-changing neutral current decays, B → K ℓ +ℓ- and B → K*(892)ℓ+ℓ- with mℓℓ > 0.5 GeV. (2) The lepton-flavor-violating decays, B → h e+/-mu ∓, B+ → h -e+e +, B+ → h -e+mu+, and B+ → h-mu +mu+, where h is pi, K, rho and K*(892), a total of sixteen modes. (3) The lepton-flavor-violating leptonic decays including tau lepton, B0 → mu+/-tau ∓ and B0 → e +/-tau∓.; We find no evidence for these decays, and place 90% confidence level upper limits on their branching fractions: (1) B (B → K ℓ+ℓ -) < 1.7 x 10-6 and B (B → K*ℓ+ℓ -) mℓℓ > 0.5GeV < 3.3 x 10-6. (2) B (B → h ℓ ℓ) upper limits range from 1.0 to 8.0 x 10-6. (3) B (B0 → mu+/-tau ∓) < 3.8 x 10-5 and B (B0 → e +/-tau∓) < 1.3 x 10-4 . |