Experiments on the cuprate superconductors demonstrate that these materials may be viewed as a stack of Josephson junctions along the direction normal to the CuO 2 planes (the c-axis). In this paper, we present a model which describes this intrinsic Josephson coupling in terms of incoherent quasiparticle hopping along the c-axis arising from wave-function overlap, impurity-assisted hopping, and boson-assisted hopping. We use this model to compute the magnitude and temperature T dependence of the resulting Josephson critical current j c (T for s- and d-wave superconductors. Contrary to other approaches, d-wave pairing in this model is compatible with an intrinsic Josephson effect at all hole concentrations and leads to j c (T T at low T. By parameterizing our theory with c-axis resistivity data from YBa 2 Cu 3 O 7 - δ (YBCO), we estimate i c (T for optimally doped and underdoped members of this family. j c (T) can be measured either directly or indirectly through microwave penetration depth experiments, and current measurements on Bi 2 Sr 2 CaCu 2 O 8 and La 2 - x Sr x CuO 4 are found to be consistent with s-wave pairing and the dominance of assisted hopping processes. The situation in YBCO is still unclear, but our estimates suggest that further experiments on this compound would be of great help in elucidating the validity of our model in general and the pairing symmetry in particular.