Nine empirical correlations for the calculation of the liquid saturation density of pure fluids are studied for their accuracy and applicability. All of them are based on the corresponding states principle, and we have included very recent proposals. The first model requires only the knowledge of critical parameters, the following seven need the critical parameters and acentric factor as inputs, and the last requires the Lennard-Jones molecular parameters and the acentric factor as input data. As a reference, we take the numerical values for the liquid saturation density accepted by the DIPPR project for 552 fluids, grouped into 30 families. Recommendations are given for the use of each model and for the choice of the adequate model for each family of fluids, including for particular fluids.