This paper presents a comparison of surface hopping and mean field approaches for simulating proton transfer reactions. In these mixed quantum/classical simulations, the transferring proton(s) are treated quantum mechanically, while the remaining nuclei are treated classically. The surface hopping method used for these calculations is the molecular dynamics with quantum transitions (MDQT) method based on Tully's fewest switches algorithm. In addition, this paper describes a modified MDQT method (denoted MDQT*) that eliminates classically forbidden transitions to promote consistency between the quantum probabilities and the fraction of trajectories in each adiabatic state. The MDQT, MDQT*, mean field, and fully quantum dynamical methods are applied to one-dimensional model single and double proton transfer reactions. Both the MDQT and MDQT* calculations agree remarkably well with the fully quantum dynamical calculations, while the mean field calculations exhibit qualitatively incorrect behavior.