Non-volatile resistive switching (NVRS) is a widely available effect in transitional metal oxides, colloquially known as memristors, and of broad interest for memory technology and neuromorphic computing. Until recently, NVRS was not known in other transitional metal dichalcogenides (TMDs), an important material class owing to their atomic thinness enabling the ultimate dimensional scaling. Here, various monolayer or few-layer 2D materials are presented in the conventional vertical structure that exhibit NVRS, including TMDs (MX , M = transitional metal, e.g., Mo, W, Re, Sn, or Pt; X = chalcogen, e.g., S, Se, or Te), TMD heterostructure (WS /MoS ), and an atomically thin insulator (h-BN). These results indicate the universality of the phenomenon in 2D non-conductive materials, and feature low switching voltage, large ON/OFF ratio, and forming-free characteristic. A dissociation-diffusion-adsorption model is proposed, attributing the enhanced conductance to metal atoms/ions adsorption into intrinsic vacancies, a conductive-point mechanism supported by first-principle calculations and scanning tunneling microscopy characterizations. The results motivate further research in the understanding and applications of defects in 2D materials.