Most diffraction-unlimited super-resolution imaging critically depends on the switching of fluorophores between at least two states, often induced using intense laser light and specialized buffers or UV radiation. Recently, so-called self-blinking dyes that switch spontaneously between an open, fluorescent "on" state and a closed, colorless "off" state were introduced. Here, we exploit the synergy between super-resolution optical fluctuation imaging (SOFI) and spontaneously switching fluorophores for 2D and 3D imaging. SOFI analyzes higher order statistics of fluctuations in the fluorophore emission instead of localizing individual molecules. It thereby tolerates a broad range of labeling densities, switching behavior, and probe brightness. Thus, even dyes that exhibit spontaneous blinking characteristics that are not suitable or suboptimal for single molecule localization microscopy can be used successfully for SOFI-based super-resolution imaging. We demonstrate 2D imaging of fixed cells with almost uniform resolution up to 50-60 nm in 6th order SOFI and characterize changing experimental conditions. Next, we investigate volumetric imaging using biplane and eight-plane data acquisition. We extend 3D cross-cumulant analysis to 4th order, achieving super-resolution in 3D with up to 29 depth planes. Finally, the low laser excitation intensities needed for single and biplane self-blinking SOFI are well suited for live-cell imaging. We show the perspective for time-resolved imaging by observing slow membrane movements in cells. Self-blinking SOFI thus provides a more robust alternative route for easy-to-use 2D and 3D high-resolution imaging.