Most general force fields only implement a harmonic potential to model covalent bonds. In addition, in some force fields, all or a selection of the covalent bonds are constrained in molecular dynamics simulations. Nevertheless, it is possible to implement accurate bond potentials for a relatively small computational cost. Such potentials may be important for spectroscopic applications, free energy perturbation calculations or for studying reactions using empirical valence bond theory. Here, we evaluate different bond potentials for diatomic molecules. Based on quantum-chemical scans around the equilibrium distance of 71 molecules using the MP2/aug-cc-pVTZ level of theory as well as CCSD(T) with the same basis-set, we determine the quality of fit to the data of 28 model potentials. As expected, a large spread in accuracies of the potentials is found and more complex potentials generally provide a better fit. As a second and more challenging test, five spectroscopic parameters (ωe, ωexe, αe, Be and De) predicted based on quantum chemistry as well as the fitted potentials are compared to experimental data. A handful of the 28 potentials tested are found to be accurate. Of these, we suggest that the potential due to Hua (Phys. Rev. A, 42 (1990), 2524) could be a suitable choice for implementation in molecular simulations codes, since it is considerably more accurate than the well-known Morse potential (Phys. Rev., 34 (1929), 57) at a very similar computational cost.