We compute a large grid of photoionization models that covers a wide range of physical parameters and is representative of most of the observed planetary nebulae (PNe). Using this grid, we derive new formulae for the ionization correction factors (ICFs) of He, O, N, Ne, S, Ar, Cl, and C. Analytical expressions to estimate the uncertainties arising from our ICFs are also provided. This should be useful since these uncertainties are usually not considered when estimating the error bars in element abundances. Our ICFs are valid over a variety of assumptions such as the input metallicities, the spectral energy distribution of the ionizing source, the gas distribution, or the presence of dust grains. Besides, the ICFs are adequate both for large aperture observations and for pencil-beam observations in the central zones of the nebulae. We test our ICFs on a large sample of observed PNe that extends as far as possible in ionization, central star temperature, and metallicity, by checking that the Ne/O, S/O, Ar/O, and Cl/O ratios show no trend with the degree of ionization. Our ICFs lead to significant differences in the derived abundance ratios as compared with previous determinations, especially for N/O, Ne/O, and Ar/O.