(Abridged) In this paper we present a compilation of results from our most advanced neutron star merger simulations, including a description of the employed numerical procedures and a more complete overview over a large number of computed models. The three-dimensional hydrodynamic simulations were done with a code based on the Piecewise Parabolic Method with up to five levels of nested Cartesian grids. The simulations are basically Newtonian, but gravitational-wave emission and the corresponding back-reaction are taken into account. The use of a physical nuclear equation of state allows us to follow the thermodynamic history of the stellar medium and to compute the energy and lepton number loss due to the emission of neutrinos. The computed models differ concerning the neutron star masses and mass ratios, the neutron star spins, the numerical resolution expressed by the cell size of the finest grid and the number of grid levels, and the calculation of the temperature from the solution of the entropy equation instead of the energy equation. Our simulations show that the details of the gravitational-wave emission are still sensitive to the numerical resolution, even in our highest-quality calculations. The amount of mass which can be ejected from neutron star mergers depends strongly on the angular momentum of the system. Our results do not support the initial conditions of temperature and proton-to-nucleon ratio assumed in recent work for producing a solar r-process pattern for nuclei around and above the A approx 130 peak. The improved models confirm our previous conclusion that gamma-ray bursts are not powered by neutrino emission during the dynamical phase of the merging of two neutron stars.
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