CCD photometry of 18 Jupiter family comets, observed at medium and large heliocentric distances, was carried out between April 1990 and July 1995. This is part of a long-term observational program designed to obtain their nuclear magnitudes. The observations were made with the 1.54-m Danish Telescope at ESO La Silla, the 2.5-m Nordic Optical Telescope (NOT) at Observatorio del Roque de los Muchachos (La Palma), the 2.0-m telescope at Pic du Midi, and the 2.15-m telescope at CASLEO, Argentina. Our estimates of the absolute nuclear magnitudes are discussed in comparison with previous determinations. Estimates (sometimes upper limits) for the effective radius (R) of the nuclei are computed considering a typical geometric albedo pv=0.04. The lowest radius found is the one of 37P/Forbes (R=1.0 km) while the largest corresponds to 65P/Gunn (R=11.0 km), but in this case the comet was observed very active. Wherever possible, cometary image profiles are compared with stellar profiles, in order to determine the existence of a faint coma. Seven of the comets were active, six of them at heliocentric distances larger than 4 AU. This unexpected activity is also discussed. We find a strong correlation between activity at large heliocentric distances and recent downward jumps in perihelion distance.