We have used the Visible Multi-Object Spectrograph (VIMOS) integral field spectrograph to map the emission-line properties in a sample of 24 star-forming galaxies selected from the Sloan Digital Sky Survey (SDSS) data base. In this paper we present and describe the sample, and explore some basic properties of SDSS galaxies with resolved emission-line fields. We fit the Ha+[N II] emission lines in each spectrum to derive maps of continuum, Ha flux, velocity and velocity dispersion. The Ha, Hß, [N II] and [O III] emission lines are also fit in summed spectra for circular annuli of increasing radius. A simple mass model is used to estimate dynamical mass within 10 kpc, which compared to estimates of stellar mass shows that between 10 and 100 per cent of total mass is in stars. We present plots showing the radial behaviour of equivalent width (EW)[Ha], u-i colour and emission-line ratios. Although EW[Ha] and u-i colour trace current or recent star formation, the radial profiles are often quite different. Whilst line ratios do vary with annular radius, radial gradients in galaxies with central line ratios typical of active galactic nucleus (AGN) or low-ionization nuclear emission-line regions are mild, with a hard component of ionization required out to large radii. We use our VIMOS maps to quantify the fraction of Ha emission contained within the SDSS fibre, taking the ratio of total Ha flux to that of a simulated SDSS fibre. A comparison of the flux ratios to colour-based SDSS extrapolations shows a 175 per cent dispersion in the ratio of estimated to actual corrections in normal star-forming galaxies, with larger errors in galaxies containing AGN. We find a strong correlation between indicators of nuclear activity: galaxies with AGN-like line ratios and/or radio emission frequently show enhanced dispersion peaks in their cores, requiring non-thermal sources of heating. Altogether, about half of the galaxies in our sample show no evidence for nuclear activity or non-thermal heating. The fully reduced data cubes and the maps with the line-fit results are available as FITS files from the authors.