The most promising source of gravitational waves for the planned detectors LIGO and VIRGO are merging compact binaries, i.e., neutron star/neutron star (NS/NS), neutron star/black hole (NS/BH), and black hole/black-hole (BH/BH) binaries. We investigate how accurately the distance to the source and the masses and spins of the two bodies will be measured from the gravitational wave signals by the three detector LIGO/VIRGO network using ``advanced detectors'' (those present a few years after initial operation). The combination \({\cal M} \equiv (M_1 M_2)^{3/5}(M_1 +M_2)^{-1/5}\) of the masses of the two bodies is measurable with an accuracy \(\approx 0.1\%-1\%\). The reduced mass is measurable to \(\sim 10\%-15\%\) for NS/NS and NS/BH binaries, and \(\sim 50\%\) for BH/BH binaries (assuming \(10M_\odot\) BH's). Measurements of the masses and spins are strongly correlated; there is a combination of \(\mu\) and the spin angular momenta that is measured to within \(\sim 1\%\). We also estimate that distance measurement accuracies will be \(\le 15\%\) for \(\sim 8\%\) of the detected signals, and \(\le 30\%\) for \(\sim 60\%\) of the signals, for the LIGO/VIRGO 3-detector network.