Silicon-based plasmonic waveguides can be used to simultaneously transmit electrical signals and guide optical energy with deep subwavelength localization, thus providing us with a well needed connecting link between contemporary nanoelectronics and silicon photonics. In this paper, we examine the possibility of employing the large third-order nonlinearity of silicon to create active and passive photonic devices with silicon-based plasmonic waveguides. We unambiguously demonstrate that the relatively weak dependance of the Kerr effect, two-photon absorption (TPA), and stimulated Raman scattering on optical intensity, prevents them from being useful in μm-long plasmonic waveguides. On the other hand, the TPA-initiated free-carrier effects of absorption and dispersion are much more vigorous, and have strong potential for a variety of practical applications. Our work aims to guide research efforts towards the most promising nonlinear optical phenomena in the thriving new field of silicon-based plasmonics.