We search for the flavor-changing neutral-current decays B → K ( * ) ν ¯ ν , and the invisible decays J / ψ → ν ¯ ν and ψ ( 2 S ) → ν ¯ ν via B → K ( * ) J / ψ and B → K ( * ) ψ ( 2 S ) , respectively, using a data sample of 471 × 10 6 B ¯¯¯ B pairs collected by the BABAR experiment. We fully reconstruct the hadronic decay of one of the B mesons in the Υ ( 4 S ) → B ¯¯¯ B decay, and search for the B → K ( * ) ν ¯ ν 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 + ν ¯ ν ) < 3.7 × 10 − 5 , B ( B 0 → K 0 ν ¯ ν ) < 8.1 × 10 − 5 , B ( B + → K * + ν ¯ ν ) < 11.6 × 10 − 5 , B ( B 0 → K * 0 ν ¯ ν ) < 9.3 × 10 − 5 , and combined upper limits of B ( B → K ν ¯ ν ) < 3.2 × 10 − 5 and B ( B → K ∗ ν ¯ ν ) < 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 → ν ¯ ν ) < 3.9 × 10 − 3 and B ( ψ ( 2 S ) → ν ¯ ν ) < 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 ( * ) ν ¯ ν decays over the full kinematic spectrum.