We use near-field Raman imaging and spectroscopy to study localized vibrational modes along individual, single-walled carbon nanotubes (SWNTs) with a spatial resolution of 10-20 nm. Our approach relies on the enhanced field near a laser-irradiated gold tip which acts as the Raman excitation source. We find that for arc-discharge SWNTs, both the radial breathing mode (RBM) and intermediate frequency mode (IFM) are highly localized. We attribute such localization to local changes in the tube structure (n, m). In comparison, we observe no such localization of the Raman active modes in SWNTs grown by chemical vapor deposition (CVD). The direct comparison between arc-discharge and CVD-grown tubes allows us to rule out any artifacts induced by the supporting substrate.