We investigate the well-known correlations between the dynamical mass-to-light ratio (M/L) and other global observables of elliptical (E) and lenticular (S0) galaxies. We construct two-integral Jeans and three-integral Schwarzschild dynamical models for a sample of 25 E/S0 galaxies with SAURON integral-field stellar kinematics to about one effective (half-light) radius Re. They have well-calibrated I-band Hubble Space Telescope WFPC2 and large-field ground-based photometry, accurate surface brightness fluctuation distances, and their observed kinematics is consistent with an axisymmetric intrinsic shape. All these factors result in an unprecedented accuracy in the M/L measurements. We find a tight correlation of the form (M/L) = (3.80 +/- 0.14) × (σe/200kms-1)0.84+/-0.07 between the M/L (in the I band) measured from the dynamical models and the luminosity-weighted second moment σe of the LOSVD within Re. The observed rms scatter in M/L for our sample is 18 per cent, while the inferred intrinsic scatter is ~13 per cent. The (M/L)-σe relation can be included in the remarkable series of tight correlations between σe and other galaxy global observables. The comparison of the observed correlations with the predictions of the Fundamental Plane (FP), and with simple virial estimates, shows that the `tilt' of the FP of early-type galaxies, describing the deviation of the FP from the virial relation, is almost exclusively due to a real M/L variation, while structural and orbital non-homology have a negligible effect. When the photometric parameters are determined in the `classic' way, using growth curves, and the σe is measured in a large aperture, the virial mass appears to be a reliable estimator of the mass in the central regions of galaxies, and can be safely used where more `expensive' models are not feasible (e.g. in high-redshift studies). In this case the best-fitting virial relation has the form (M/L)vir= (5.0 +/- 0.1) ×Reσ2e/(LG), in reasonable agreement with simple theoretical predictions. We find no difference between the M/L of the galaxies in clusters and in the field. The comparison of the dynamical M/L with the (M/L)pop inferred from the analysis of the stellar population, indicates a median dark matter fraction in early-type galaxies of ~30 per cent of the total mass inside one Re, in broad agreement with previous studies, and it also shows that the stellar initial mass function varies little among different galaxies. Our results suggest a variation in M/L at constant (M/L)pop, which seems to be linked to the galaxy dynamics. We speculate that fast-rotating galaxies have lower dark matter fractions than the slow-rotating and generally more-massive ones. If correct, this would suggest a connection between the galaxy assembly history and the dark matter halo structure. The tightness of our correlation provides some evidence against cuspy nuclear dark matter profiles in galaxies.