Confining light by plasmonic waveguides is promising for miniaturizing optical components, while topological photonics has been explored for robust light localization. Here we propose combining the two approaches into a simple periodically perforated plasmonic waveguide (PPW) design exhibiting robust localization of long-range surface plasmon polaritons. We predict the existence of a topological edge state originating from a quantized topological invariant, and numerically demonstrate the viability of its excitation at telecommunication wavelength using near-field and waveguide-based approaches. Strong modification of the radiative lifetime of dipole emitters by the edge state, and its robustness to disorder, are demonstrated.