We present 2-D arrays of plasmonic nanostructures ─ gold nanopillars on a gold coated substrate ─ coated with a thin film of VO2 (vanadium dioxide), as novel optical switches. The incident optical radiation is coupled into plasmonic modes due to the small gaps between the adjacent nanostructures, which leads to high electromagnetic fields in the gap regions. As VO2 changes phase from the semiconducting to the metallic phase on heating or on application of voltage, there is a change in the overall plasmonic properties of the VO2 coated 2-D plasmonic nanostructures, and a change in the reflectance spectra. We employ Rigorous Coupled Wave Analysis (RCWA) to calculate the switchability, i.e., the differential reflectance between the semiconducting and metallic state of the VO2 coated nanostructures. An exhaustive analysis of the differential reflectance spectra is carried out, by optimizing the different geometrical parameters of the structure. Moreover, we demonstrate that these 2-D arrays of plasmonic nanostructures can be employed for switching with unpolarized light. These nanostructures can also be employed for multi-wavelength switching if a degree of asymmetry is introduced with different gaps or periodicities in the two dimensions. Thus, we propose 2-D VO2 coated nanostructures which can be employed as plasmonic switches with unpolarized light.