Simulations of diffusion in neural tissues have traditionally been limited to analytical solutions, to grid-based solvers, or to small-scale Monte Carlo simulations. None of these approaches has had the capability to simulate realistic complex neural tissues on the scale of even a single voxel of reasonable (i.e., clinical) size. An approach is described that combines a Monte Carlo Brownian dynamics simulator capable of simulating diffusion in arbitrarily complex polygonal geometries with a signal integrator flexible enough to handle a variety of pulse sequences. Taken together, this package provides a complete and general simulation environment for diffusion MRI experiments. The simulator is validated against analytical solutions for unbounded diffusion and diffusion between parallel plates. Further results are shown for aligned fibers, varying packing density and permeability, and for crossing straight fibers.