Control over the interaction between single photons and individual optical emitters is an outstanding problem in quantum science and engineering. It is of interest for ultimate control over light quanta, as well as for potential applications such as efficient photon collection, single-photon switching and transistors, and long-range optical coupling of quantum bits. Recently, substantial advances have been made towards these goals, based on modifying photon fields around an emitter using high-finesse optical cavities. Here we demonstrate a cavity-free, broadband approach for engineering photon-emitter interactions via subwavelength confinement of optical fields near metallic nanostructures. When a single CdSe quantum dot is optically excited in close proximity to a silver nanowire, emission from the quantum dot couples directly to guided surface plasmons in the nanowire, causing the wire's ends to light up. Non-classical photon correlations between the emission from the quantum dot and the ends of the nanowire demonstrate that the latter stems from the generation of single, quantized plasmons. Results from a large number of devices show that efficient coupling is accompanied by more than 2.5-fold enhancement of the quantum dot spontaneous emission, in good agreement with theoretical predictions.