We present the emission-line fluxes and kinematics of 48 representative elliptical and lenticular galaxies obtained with our custom-built integral-field spectrograph, SAURON, operating on the William Herschel Telescope. Hβ, [OIII]λλ4959,5007 and [NI]λλ5198,5200 emission lines were measured using a new procedure that simultaneously fits both the stellar spectrum and the emission lines. Using this technique we can detect emission lines down to an equivalent width of 0.1 Å set by the current limitations in describing galaxy spectra with synthetic and real stellar templates, rather than by the quality of our spectra. Gas velocities and velocity dispersions are typically accurate to within 14 and 20 km s-1, respectively, and at worse to within 25 and 40 km s-1. The errors on the flux of the [OIII] and Hβ lines are on average 10 and 20 per cent, respectively, and never exceed 30 per cent. Emission is clearly detected in 75 per cent of our sample galaxies, and comes in a variety of resolved spatial distributions and kinematic behaviours. A mild dependence on the Hubble type and galactic environment is observed, with higher detection rates in lenticular galaxies and field objects. More significant is the fact that only 55 per cent of the galaxies in the Virgo cluster exhibit clearly detected emission. The ionized-gas kinematics is rarely consistent with simple coplanar circular motions. However, the gas almost never displays completely irregular kinematics, generally showing coherent motions with smooth variations in angular momentum. In the majority of the cases, the gas kinematics is decoupled from the stellar kinematics, and in half of the objects this decoupling implies a recent acquisition of gaseous material. Over the entire sample however, the distribution of the mean misalignment values between stellar and gaseous angular momenta is inconsistent with a purely external origin. The distribution of kinematic misalignment values is found to be strongly dependent on the apparent flattening and the level of rotational support of galaxies, with flatter, fast rotating objects hosting preferentially corotating gaseous and stellar systems. In a third of the cases, the distribution and kinematics of the gas underscore the presence of non-axisymmetric perturbations of the gravitational potential. Consistent with previous studies, the presence of dust features is always accompanied by gas emission while the converse is not always true. A considerable range of values for the [OIII]/Hβ ratio is found both across the sample and within single galaxies. Despite the limitations of this ratio as an emission-line diagnostic, this finding suggests either that a variety of mechanisms is responsible for the gas excitation in E and S0 galaxies or that the metallicity of the interstellar material is quite heterogeneous.