  We present new (3+1) dimensional numerical relativity simulations of the
binary neutron star (BNS) mergers that take into account the NS spins. We
consider different spin configurations, aligned or antialigned to the orbital
angular momentum, for equal and unequal mass BNS and for two equations of
state. All the simulations employ quasiequilibrium circular initial data in the
constant rotational velocity approach, i.e. they are consistent with Einstein
equations and in hydrodynamical equilibrium. We study the NS rotation effect on
the energetics, the gravitational waves (GWs) and on the possible
electromagnetic (EM) emission associated to dynamical mass ejecta. For
dimensionless spin magnitudes of $\chi\sim0.1$ we find that spin-orbit
interactions and also spin-induced-quadrupole deformations affect the
late-inspiral-merger dynamics. The latter is, however, dominated by finite-size
effects. Spin (tidal) effects contribute to GW phase differences up to 5 (20)
radians accumulated during the last eight orbits to merger. Similarly, after
merger the collapse time of the remnant and the GW spectrogram are affected by
the NSs rotation. Spin effects in dynamical ejecta are clearly observed in
unequal mass systems in which mass ejection originates from the tidal tail of
the companion. Consequently kilonovae and other EM counterparts are affected by
spins. We find that spin aligned to the orbital angular momentum leads to
brighter EM counterparts than antialigned spin with luminosities up to a factor
of two higher.
