The combination of modern nanofabrication techniques and advanced computational tools has opened unprecedented opportunities to mold the flow of light. In particular, discrete photonic structures can be designed such that the resulting light dynamics mimics quantum mechanical condensed matter phenomena. By mapping the time-dependent probability distribution of an electronic wave packet to the spatial light intensity distribution in the corresponding photonic structure, the quantum mechanical evolution can be visualized directly in a coherent, yet classical wave environment. On the basis of this approach, several groups have recently observed discrete diffraction, Bloch oscillations and Zener tunnelling in different dielectric structures. Here we report the experimental observation of discrete diffraction and Bloch oscillations of surface plasmon polaritons in evanescently coupled plasmonic waveguide arrays. The effective external potential is tailored by introducing an appropriate transverse index gradient during nanofabrication of the arrays. Our experimental results are in excellent agreement with numerical calculations.