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The intercalation of ions into layered compounds has long been exploited in energy storage devices such as batteries and electrochemical capacitors. However, few host materials are known for ions much larger than lithium. We demonstrate the spontaneous intercalation of cations from aqueous salt solutions between two-dimensional (2D) Ti₃C₂ MXene layers. MXenes combine 2D conductive carbide layers with a hydrophilic, primarily hydroxyl-terminated surface. A variety of cations, including Na⁺, K⁺, NH₄⁺, Mg²⁺, and Al³⁺, can also be intercalated electrochemically, offering capacitance in excess of 300 farads per cubic centimeter (much higher than that of porous carbons). This study provides a basis for exploring a large family of 2D carbides and carbonitrides in electrochemical energy storage applications using single- and multivalent ions.