Mass production of high-quality graphene sheets is essential for their practical application in electronics, optoelectronics, composite materials, and energy-storage devices. Here we report a prompt electrochemical exfoliation of graphene sheets into aqueous solutions of different inorganic salts ((NH4)(2)SO4, Na2SO4, K2SO4, etc.). Exfoliation in these electrolytes leads to graphene with a high yield (>85%, <= 3 layers), large lateral size (up to 44 mu m), low oxidation degree (a C/O ratio of 17.2), and a remarkable hole mobility of 310 cm(2) V-1 s(-1). Further, highly conductive graphene films (11 Omega sq(-1)) are readily fabricated on an A4-size paper by applying brush painting of a concentrated graphene ink (10 mg mL(-1), in N,N'-dimethylformamide). All-solid-state flexible supercapacitors manufactured on the basis of such graphene films deliver a high area capacitance of 11.3 mF cm(-2) and an excellent rate capability of 5000 mV s(-1). The described electrochemical exfoliation shows great promise for the industrial-scale synthesis of high-quality graphene for numerous advanced applications.