LAMMPS and GROMACS are popular simulation packages for molecular dynamics (MD) simulations. Both can be used to simulate Brownian Dynamics by using Langevin dynamics. See “fix langevin” in LAMMPS or “bd integrator” in GROMACS.
GROMACS Tutorial: http://www.gromacs.org/WIKI-import/Main_Page/Tutorials
SMOG: Structure-based Models for Biomolecules: http://smog-server.org/
BDpack is a Brownian dynamics package developed recently. It is an open source code and is written in parallel with high computational efficiency. It can be found at: http://amir-saadat.github.io/BDpack/