Over the past decade, the significance of two-dimensional (2D) atomic sheets has been fully demonstrated by a series of fascinating performances in electronic, photonic, and phononic nanotechnology including topologically-protected charge transport, spatially-separated excitons, and strongly anisotropic heat transport, respectively. Among various 2D materials, transitional metal dichalcogenides (TMDs) stand out due to their unique band gap, high mobility, and quantum confinement. In this work, a novel non-volatile resistive switching (NVRS) phenomenon is presented in the typical (MX₂, M=Mo, W; and X=S, Se) transitional metal dichalcogenides (TMDs) single-layer atomic sheets in vertical metal-insulator-metal (MIM) structure. The intriguing findings subvert the traditional thinking that resistance switching is not accessible down to sub-nanometer scale owing to excessive leakage currents. Stable forming-free unipolar and bipolar operations are demonstrated under ambient condition at room temperature, with desirable transition voltage, large on/off ratio and promising reliability. Emerging device concepts in non-volatile flexible memory fabrics, zero static power radio-frequency switches, and neuromorphic computing could be inspired substantially from the universal NVRS effect in atomristor (in essence, memristor in single atomic sheet) and the associated wide materials space and electrode co-engineering for particular applications.