A catalog of a sample of 105 Jupiter family (JF) comets (defined as those with Tisserand constants T > 2 and orbital periods P < 20 yr) is presented with our ``best estimates'' of their absolute nuclear magnitudes H_N = V(1,0,0). The catalog includes all the nuclear magnitudes reported after 1950 until August 1998 that appear in the International Comet Quarterly Archive of Cometary Photometric Data, the Minor Planet Center (MPC) data base, IAU Circulars, International Comet Quarterly, and a few papers devoted to some particular comets, together with our own observations. Photometric data previous to 1990 have mainly been taken from the Comet Light Curve Catalogue (CLICC) compiled by Kamél (cite{kamel}). We discuss the reliability of the reported nuclear magnitudes in relation to the inherent sources of errors and uncertainties, in particular the coma contamination often present even at large heliocentric distances. A large fraction of the JF comets of our sample indeed shows various degrees of activity at large heliocentric distances, which is correlated with recent downward jumps in their perihelion distances. The reliability of coma subtraction methods to compute the nuclear magnitude is also discussed. Most absolute nuclear magnitudes are found in the range 15 - 18, with no magnitudes fainter than H_N ~ 19.5. The catalog can be found at: http://www.fisica.edu.uy/ ~ gonzalo/catalog/. Table 2 and Appendix B are only available in electronic form at http://www.edpsciences.org Table 5 is also available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html