We present the first set of a new generation of models of massive stars with a solar composition extending between 13 and 120M_{sun}, computed with and without the effects of rotation. We included two instabilities induced by rotation: the meridional circulation and the shear instability. We implemented two alternative schemes to treat the transport of the angular momentum: the advection-diffusion formalism and the simpler purely diffusive one. The full evolution from the pre-main sequence up to the pre-supernova stage is followed in detail with a very extended nuclear network. The explosive yields are provided for a variety of possible mass cuts and are available at the Web site http://www.iasf-roma.inaf.it/orfeo/public_html. We find that both the He and the CO core masses are larger than those of their non-rotating counterparts. Also the C abundance left by the He burning is lower than in the non-rotating case, especially for stars with an initial mass of 13-25M{sun}, and this affects the final mass-radius relation, basically the final binding energy, at the pre-supernova stage. The elemental yields produced by a generation of stars rotating initially at 300km/s do not change substantially with respect to those produced by a generation of non-rotating massive stars, the main differences being a slight overproduction of the weak s-component and a larger production of F. Since rotation also affects the mass-loss rate, either directly or indirectly, we find substantial differences in the lifetimes as O-type and Wolf-Rayet subtypes between the rotating and non-rotating models. The maximum mass exploding as Type IIP supernova ranges between 15 and 20M {sun}_ in both sets of models (this value depends basically on the larger mass-loss rates in the red supergiant phase due to the inclusion of the dust-driven wind). This limiting value is in remarkably good agreement with current estimates.