Calculation of molecular geometries and harmonic vibrational frequencies are pre-requisites for thermochemistry calculations. Contrary to conventional wisdom, this paper demonstrates that quantum chemical predictions of the thermochemistry of many gas and solution phase chemical reactions appear to be very insensitive to the choice of basis sets. For a large test set of 80 diverse organic and transition-metal-containing reactions, variations in reaction free energy based on geometries and frequencies calculated using a variety of double and triple-zeta basis sets from the Pople, Jensen, Ahlrichs, and Dunning families are typically less than 4 kJ mol-1, especially when the quasiharmonic oscillator correction is applied to mitigate the effects of low-frequency modes. Our analysis indicates that for many organic molecules and their transition states, high-level revDSD-PBEP86-D4 and DLPNO-CCSD(T)/(aug-)cc-pVTZ single-point energies usually vary by less than 2 kJ mol-1 on density functional theory geometries optimized using basis sets ranging from 6-31+G(d) to aug-pcseg-2 and aug-cc-pVTZ. In cases where these single-point energies vary significantly, indicating sensitivity of molecular geometries to the choice of basis set, there is often substantial cancellation of errors when the reaction energy or barrier is calculated. The study concludes that the choice of basis set for molecular geometry and frequencies, particularly those considered in this study, is not critical for the accuracy of thermochemistry calculations in the gas or solution phase.