We search for the flavor-changing neutral-current decays B→K(*) νν̄, and the invisible decays J/ψ→νν̄ and ψ(2S)→νν̄ via B→K(*) J/ψ and B→K(*) ψ(2S), respectively, using a data sample of 471×106 BB̄ pairs collected by the BABAR experiment. We fully reconstruct the hadronic decay of one of the B mesons in the Υ(4S)→BB̄ decay, and search for the B→K(*) νν̄ decay in the rest of the event. We observe no significant excess of signal decays over background and report branching fraction upper limits of B(B+→K +νν̄)<3.7×10-5, B(B0→K0νν ̄)<8.1×10-5, B(B+→K *+νν̄)<11.6×10-5, B(B0→K*0νν̄)<9.3×10-5, and combined upper limits of B(B→Kνν̄)<3.2×10-5 and B(B→K*νν̄)<7.9×10-5, all at the 90% confidence level. For the invisible quarkonium decays, we report branching fraction upper limits of B(J/ψ→νν̄)<3. 9×10-3 and B(ψ(2S)→νν̄)<15. 5×10-3 at the 90% confidence level. Using the improved kinematic resolution achieved from hadronic reconstruction, we also provide partial branching fraction limits for the B→K(* νν̄ decays over the full kinematic spectrum. © 2013 American Physical Society.