In this paper, periodic arrays of identical V-shaped gold nanostructures and variable V-shaped gold nanostructures are designed on top of a gold-coated silicon dioxide (SiO2) substrate with a thin spacer layer of vanadium dioxide (VO2) to realize multi-wavelength and broadband plasmonic switches, respectively. The periodic array of identical V-shaped nanostructures (IVNSs) with small inter-particle separation leads to coupled interactions of the elementary plasmons of a V-shaped nanostructure (VNS), resulting in a hybridized plasmon response with two longitudinal plasmonic modes in the reflectance spectra of the proposed switches when the incident light is polarized in the x-direction. The x-direction is oriented along the axis that joins the V-junctions of all VNSs in one unit cell of the periodic array. On exposure to temperature, electric field, or optical stimulus, the VO2 layer transforms from its monoclinic semiconducting state to its rutile metallic state, leading to an overall change in the reflectance spectra obtained from the proposed nanostructures and resulting in an efficient multi-wavelength switching action. Finite difference time domain (FDTD) modelling is employed to demonstrate that an extinction ratio > 12 dB at two wavelengths can be achieved by employing the proposed switches by employing periodic arrays of identical V-shaped nanostructures. Further, plasmonic switches based on variable V-shaped nanostructures (VVNSs) — i.e., multiple VNSs with variable arm lengths in one unit cell of a periodic array — are proposed for broadband switching. In the broadband operation mode, we report an extinction ratio > 5 dB over an operational wavelength range > 1400 nm in the near-IR spectral range spanning over all optical communication bands, i.e., the O, E, S, C, L and U bands. Further, it is also demonstrated that the wavelength of operation for these switches can be tuned by varying the geometrical parameters of the proposed switches. These switches have the potential to be employed in communication networks where ultrasmall and ultrafast switches with multi-wavelength operation or switching over a wide operational bandwidth are inevitably required.