We present the development and verification of a Monte Carlo binary collision model for simulating elastic and inelastic collisions in particle-in-cell simulations. We apply the corrected binary collision model originally developed for charged-particles collisions to all considered scattering channels, including Coulomb collisions, elastic neutral–neutral and charged–neutral collisions, ionization, excitation, and fusion. The model's implementation is described and verified through a series of simulations, including charged- and neutral-particle thermal equilibration, slowing of electrons in warm solid-density aluminum, collisional damping of a Langmuir wave, helium gas breakdown in an applied electric field, and thermonuclear and beam–target fusion. Then, we demonstrate the model within simulations of hydrogen plasma formation in the Princeton Field-Reversed Configuration as well as of the burning of aneutronic fusion fuel p-11B. The latter includes measurement of the fusion power density in a low-density plasma and fusion production due to the stopping of a proton ignitor beam in a compressed boron target.