We present a systematic study of the basis set dependence of the backscattering vibrational Raman intensities and Raman Optical Activity (ROA) intensity differences. The accuracies of computed Raman intensities and ROA intensity differences for a series of commonly used basis sets are reported, relative to large reference basis sets, using the B3LYP density functional. This study attempts to separately quantify the relative accuracies obtained from particular basis set combinations: one for the geometry optimization and force field computation and the other for the computation of Raman and ROA tensors. We demonstrate here that the basis set requirements for the geometry and force fields are not similar to those of the Raman and ROA tensors. The Raman and ROA tensors require basis sets with diffuse functions, while geometry optimizations and force field computations typically do not. Eleven molecules were examined: (S)-methyloxirane, (S)-methylthirane, (R)-epichlorhydrin, (S)-CHFClBr, (1S,5S)-α-pinene, (1S,5S)-β-pinene, (1S,4S)-norborneneone, (M)-σ-[4]-helicene, an enone precursor to a cytotoxic sesquiterpene, the gauche-gauche conformer of the monosaccharide methyl-β-d-glucopyranose, and the dipeptide Ac-(alanine)2-NH2. For the molecules examined here, intensities and intensity differences obtained from Raman and ROA tensors computed using the aug-cc-pVDZ basis set are nearly equivalent to those computed with the larger aug-cc-pVTZ basis set. We find that modifying the aug-cc-pVDZ basis set by removing the set of diffuse d functions on all atoms (while keeping the diffuse s and p sets), denoted as aug(sp)-cc-pVDZ, results in a basis set which is significantly faster without much reduction in the overall accuracy. In addition, the popular rDPS basis set introduced by Zuber and Hug offers a good compromise between accuracy and efficiency. The combination of either the aug(sp)-pVDZ or rDPS basis for the computation of the Raman and ROA tensors with the 6-31G* basis set for the geometry optimization and force field calculation is a reliable and cost-effective method for obtaining Raman intensities and ROA intensity differences.