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 (1985A&AS...60..425A) and Arnaud & Raymond (1992ApJ...398..394A). 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.