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A new version of the Li\`ege intranuclear cascade (INC) model is proposed for the description of spallation reactions. Compared to the previous version, it incorporates new features: (i) it can accommodate a diffuse nuclear surface, (ii) the treatment of the Pauli blocking effect is improved, removing unphysical features linked with the use of statistical blocking factors, (iii) collisions between moving spectator nucleons are explicitly suppressed, (iv) pion dynamics is improved, especially concerning the delta lifetime, (v) it can accommodate light ions as incoming projecticles, (vi) the remnant angular momentum is included in the output of the model. Another important feature is the self-consistent determination of the stopping time, i.e., the time at which the INC calculation is terminated and coupled to evaporation. The predictions of the model, used with the Schmidt evaporation code, are tested against a large body of experimental data, in the 200-MeV--2-GeV range for incident energy per nucleon, including total reaction cross sections, neutron, proton, pion, and composite double differential cross sections, particle multiplicities, residue mass and charge distributions, and residue recoil velocity distributions. Good agreement is generally obtained without additional varying parameters. It is shown that the introduction of a diffuse surface considerably improves the description of the total reaction cross sections, of the intensity of the quasielastic peak in proton and neutron double differential cross sections and of the residue production yield for isotopes close to the target. High energy neutron spectra are found to be sensitive to details of the deuteron structure in deuteron-induced reactions. The shape of the fragmentation peaks in residue mass spectra is shown to be closely related to the shape of the distribution of the excitation energy left after the cascade stage. The longitudinal residue recoil velocity and its fluctuations display typical random-walk characterics, which are interpreted as a direct consequence of the independence of successive binary collisions occurring during the cascade process and therefore provide a strong support of the basic hypotheses of the INC model. Small but systematic discrepancies between model predictions and experiment are identified and possible further improvements to reduce them are discussed. The influence of the evaporation model is investigated. A comparison with similar approaches is presented.