We compare hybrid Hartree-Fock density-functional theory to ab initio approaches for locating saddle point geometries and calculating barrier heights on a Born-Oppenhiemer potential energy surface. We located reactant, product, and saddle point stationary points for 22 reactions by the MP2 and QCISD ab initio methods and the B3LYP, BH&HLYP, mPW1PW91, and MPW1K hybrid Hartree-Fock DFT methods. We examined all of these methods with two basis sets, 6-31+G(d,p) and MG3. By comparison to calculations on five systems where the saddle point has been optimized at a high level of theory, we determined that the best saddle point geometries were obtained using the MPW1K and QCISD levels of theory. Of the methods tested, mPW!PW91 and B3LYP are the least effective for determining saddle point geometries and have mean unsigned error in barrier heights of 3.4-4.2 kcal/mol, depending on the basis set. In contrast, the MPW1K level of theory predicts the most accurate saddle point geometries and has a mean unsigned error of only 1.5 kcal/mol for either basis set. For even better accuracy, the combination of MPWlK/6-31+G(d,p) geometry calculations with QCISD(T)/MG3 or CCSD(T)/MG3 single-point energy calculations is shown to have an excellent performance-to-cost ratio. As a side product of this work, we report optimized scale factors for computing zero point energies by MPW1K.