  A class of generalized exclusion processes parametrized by the maximal
occupancy, $k\geq 1$, is investigated. For these processes with symmetric
nearest-neighbor hopping, we compute the diffusion coefficient and show that it
is independent on the spatial dimension. In the extreme cases of $k=1$ (simple
symmetric exclusion process) and $k=\infty$ (non-interacting symmetric random
walks) the diffusion coefficient is constant; for $2\leq k<\infty$, the
diffusion coefficient depends on the density and the maximal occupancy $k$. We
also study the evolution of a tagged particle. It exhibits a diffusive behavior
which is characterized by the coefficient of self-diffusion which we probe
numerically.
