An extensive study of static and dynamic Raman intensities is presented for normal vibrations of small molecules obtained with different correlated quantum chemical methods: namely, coupled-cluster, multiconfiguration self-consistent-field, and density functional theories. While this is the first systematic study of coupled-cluster (CC) Raman intensities considering also the dispersion effect for molecules with more than two atoms, another purpose of this study is the analysis of the accuracy of density functional Raman activities with respect to those from highly correlated ab initio methods in order to evaluate the validity of density functional theory for the calculation of Raman spectra for large molecules. The density functional intensities compare sufficiently well with those from ab initio methods. While the dynamic multiconfigurational intensities always compare well with the experimental values, they are usually smaller than those from density functional and coupled-cluster theories. The Raman intensities obtained from static coupled-cluster calculations are in better agreement with experiment than those from dynamic calculations, which should yield improved results as the dispersion effect is taken into account. Furthermore, Raman intensities obtained from the CC2 model are compared to those from CCSD calculations. It is found that the CC2 Raman activities deviate from the CCSD reference data. Particularly for the coupled-cluster Raman intensities the widely used Sadlej basis set leads to results which can be significantly improved on by using larger basis sets.