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We present 3D Newtonian simulations of the coalescence of two neutron stars, using a Smoothed Particle Hydrodynamics (SPH) code. We begin the simulations with the two stars in a hard, circular binary, and have them spiral together as angular momentum is lost through gravitational radiation at the rate predicted by modeling the system as two point masses. We model the neutron stars as hard polytropes ($\gamma=2.4$) of equal mass, and investigate the effect of the initial spin of the two stars on the coalescence. The process of coalescence, from initial contact to the formation of an axially symmetric object, takes only a few orbital periods. Some of the material from the two neutron stars is shed, forming a thick disk around the central, coalesced object. The mass of this disk is dependent on the initial neutron star spins; higher spin rates resulting in greater mass loss, and thus more massive disks. For spin rates that are most likely to be applicable to real systems, the central coalesced object has a mass of $2.4M_\odot$, which is tantalizingly close to the maximum mass allowed by any neutron star equation of state for an object that is supported in part by rotation. Using a realistic nuclear equation of state, we estimate the temperature of the material after the coalescence. We find that the central object is at a temperature of $\sim 10$MeV, whilst the disk is heated by shocks to a temperature of 2-4MeV.