Doping of individual single-walled carbon nanotubes via noncovalent adsorption of polyethylenimine which converts p-type semiconducting nanotubes into n-type is examined by micro-Raman studies. Distinctively different responses are observed in metallic and in semiconducting nanotubes. Very little or no changes in the radial breathing and the disorder modes are observed upon polymer adsorption on semiconducting carbon nanotubes indicating noncovalent nature of this process. Tangential G-band spectral downshift of up to similar to 10 cm(-1) without line broadening is observed for semiconducting tubes suggesting similar magnitude of electron transfer as commonly observed in electrochemical doping with alkali metals. Strong diameter dependence is also observed and can be explained by thermal ionization of charge carriers with activation barrier that scales as the energy gap of the semiconducting nanotubes. In contrast, metallic nanotubes exhibit very different behavior with significant line broadening of the G-band and concurrent enhancement of the disorder mode. In certain cases, initially symmetric Lorentzian line shapes of the G-band features with narrow line widths similar to semiconducting tubes are converted to a broad, asymmetric Breit-Wigner-Fano line shape. Implications on the effects of electron injection and the local chemical environment on the intrinsic line shape of isolated carbon nanotubes are discussed.