We highlight the emergence of metallic states in two-dimensional transition-metal-dichalcogenide nanostructures nanoribbons, islands, and inversion domain boundaries as a widespread and universal phenomenon driven by the polar discontinuities occurring at their edges or boundaries. We show that such metallic states form one-dimensional wires of electrons or holes, with a free charge density that increases with the system size, up to complete screening of the polarization charge, and can also be controlled by the specific edge or boundary configurations, e.g., through chemisorption of hydrogen or sulfur atoms at the edges. For triangular islands, local polar discontinuities occur even in the absence of a total dipole moment for the island and lead to an accumulation of free carriers close to the edges, providing a consistent explanation of previous experimental observations. To further stress the universal character of these mechanisms, we show that polar discontinuities give rise to metallic states also at inversion domain boundaries. These findings underscore the potential of engineering transition-metal-dichalcogenide nanostructures for manifold applications in nano- and optoelectronics, spintronics, catalysis, and solar-energy harvesting.