The influence of the electrode potential on the electronic structure of individual single-walled carbon nanotubes is studied using Raman spectroscopy. By analyzing the radial breathing mode intensity versus electrode potential profiles in the Raman spectra at many different laser excitation energies, we show that the charging of individual carbon nanotubes causes a broadening of the resonant Raman profiles (resonance window). This effect is observed for both a semiconducting and a metallic tube. The broadening of the resonance Raman profiles already begins at potentials where the first electronic states of a particular tube are filled or depleted. The important consequence of this effect is a striking difference between the Raman intensity versus potential profiles of metallic and semiconducting tubes. While for a metallic tube the intensity of the Raman signal is attenuated at potentials which deviate slightly from 0 V, for a semiconducting tube, the Raman intensity is significantly attenuated only after the electrode potential reaches the first van Hove singularity. Furthermore, for the metallic tube, a strong asymmetry is found in the bleaching of the Raman signal with respect to positive and negative potentials, which results from the different energy bandwidth for the pi* band and the pi band.