Results of a molecular dynamics study of several triazolium-based ionic liquids are reported. Triazolium cations include 1,2,4-triazolium, 1,2,3-triazolium, 4-amino-1,2,4-triazolium, and 1-methyl-4-amino-1,2,4-triazolium. Each cation was paired with a nitrate or perchlorate anion. These materials are part of a class of ionic compounds that have been synthesized recently but for which little physical property data are available. Properties of the more common ionic liquid, 1-n-butyl-3-methylimidazolium nitrate, are also computed and compared with the properties of the triazolium-based compounds. A molecular mechanics force field was developed for these materials using a mix of ab initio calculations and parameter fitting using the molecular compound 1H-1,2,4-triazole as a basis for the triazolium cations. Liquid-phase properties that were computed include heat capacities, cohesive energy densities, gravimetric densities/molar volumes as a function of temperature and pressure, self-diffusivities, rotational time constants, and various pair correlation functions. In the solid phase, heat capacities and lattice parameters were computed. Of all of these properties, only lattice parameters have been measured experimentally (and only for four of the triazolium compounds). The agreement with the experimental crystal structures was good. When compared with that of the imidazolium-based ionic liquid, the triazolium-based materials have much smaller molar volumes, higher cohesive energy densities, and larger specific heat capacities. They also tend to be less compressible, have a higher gravimetric density, and have faster rotational dynamics but similar translational dynamics.