Aims. The interpretation of astrophysical spectra depends directly on a knowledge of the ionization state of the emitting plasma. This is determined, in part, from collisional ionization rate coefficients. The most recent assessments of these were performed by Arnaud & Rothenflug (1985, A&AS, 60, 425) and Arnaud & Raymond (1992, ApJ, 398, 394). Since their work, new laboratory measurements of ionization cross sections have become available as well as the Flexible Atomic Code (FAC) which enables theoretical calculations of these rates. Our goal is to provide a complete set of ionization rate coefficients for the elements hydrogen through zinc. Methods. A scaling law, which assists the analysis of ionization cross sections and rate coefficients, has been developed following the approach of Burgess & Tully (1992, A&A, 254, 436). Essentially all available measured cross sections along each isoelectronic sequence have been examined and compared to cross sections calculated with the Flexible Atomic Code (FAC) and with other calculations. Two approaches has been taken to provide a complete set of ionization cross sections. In the first, fits to scaled measured ionization cross sections, particularly for neutral and singly ionized species, are performed. In the second, fits to scaled calculated direct ionization and excitation-autoionization cross sections are performed to provide the remainder of the set. The fits to the cross sections are then integrated over a Maxwellian velocity distribution to derive ionization rate coefficients. Results. A complete set of ground level ionization cross sections and rate coefficients has been developed through the combination of these two approaches. A tabulation of parameter fits to ground level ionization rate coefficients for all atoms and ions of the elements of H through Zn is provided.