Raman spectra were obtained from thin bundles containing just a few single-wall carbon nanotubes (SWNTs). These spectra exhibit new characteristics absent in the ensemble Raman measurements. A large variation in the radial breathing mode (RBM) Stokes to anti-Stokes Raman intensity ratio was observed for different metallic tubes and can be understood with a simple resonant Raman analysis. An (n, m) structural assignment for many tubes at 632 nm laser excitation was tentatively achieved on the basis of the RBM frequency and the Stokes to anti-Stokes Raman ratio. The (9, 9) armchair tube fits the simple model poorly. The varying relative intensities of different components observed in the tangential G-band Raman modes provide convincing evidence for a recently predicted chirality dependence of Raman scattering. A new Raman feature at 1417 cm-1 was assigned to achiral tubes.