Using organic transistors with a floating gate embedded in hybrid dielectrics that comprise a 2-nanometer-thick molecular self-assembled monolayer and a 4-nanometer-thick plasma-grown metal oxide, we have realized nonvolatile memory arrays on flexible plastic substrates. The small thickness of the dielectrics allows very small program and erase voltages (< or = 6 volts) to produce a large, nonvolatile, reversible threshold-voltage shift. The transistors endure more than 1000 program and erase cycles, which is within two orders of magnitude of silicon-based floating-gate transistors widely employed in flash memory. By integrating a flexible array of organic floating-gate transistors with a pressure-sensitive rubber sheet, we have realized a sensor matrix that detects the spatial distribution of applied mechanical pressure and stores the analog sensor input as a two-dimensional image over long periods of time.