A series of seven off-lattice protein models is analyzed that spans a range of chain geometry from a simple, low-resolution homopolymer model to an intermediate-resolution model that accounts for the presence of side chains, the varied character of the individual amino acids, the rigid nature of protein backbone angles, and the length scales that characterize real protein bead sizes and bond lengths. Discontinuous molecular dynamics is used to study the transition temperatures and physical structures resulting from simulations with each protein model. Our results show that each protein model undergoes multiple thermodynamic transitions that roughly correlate with protein transitions during folding to the native state. Other realistic protein behavior, such as burial of hydrophobic side chains and hindered motion due to backbone rigidity, is observed with the more-detailed models. The results suggest that, despite their simplicity when compared with all-atom protein models, the models presented here display a significant amount of protein character and, when coupled with the efficient discontinuous molecular dynamics algorithm, may enable simulation of multiprotein systems over long times.