In fluorescence microscopy, the serial acquisition of 2D images to form a 3D volume limits the maximum imaging speed. This is particularly evident when imaging adherent cells in a light-sheet fluorescence microscopy format, as their elongated morphologies require ~200 image planes per image volume. Here, by illuminating the specimen with three light-sheets, each independently detected, we present a light-efficient, crosstalk free, and volumetrically parallelized 3D microscopy technique that is optimized for high-speed (up to 14 Hz) subcellular (300 nm lateral, 600 nm axial resolution) imaging of adherent cells. We demonstrate 3D imaging of intracellular processes, including cytoskeletal dynamics in single cell migration and collective wound healing for 1500 and 1000 time points, respectively. Further, we capture rapid biological processes, including trafficking of early endosomes with velocities exceeding 10 microns per second and calcium signaling in primary neurons.