The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research. We propose an Onsager variational principle theory that describes the droplet shape evolution and predicts the deposit distribution of nonvolatile components on the substrate. It is shown that for the drying of a single droplet, the deposition pattern changes continuously from a coffee ring to volcano-like and to mountain-like depending on the mobility of the contact line and the evaporation rate. When drying of two neighbouring droplets, asymmetrical ring-like deposition patterns are formed, including fan-like and eclipse-like deposition patterns. The same theoretical model is also used to explain the multi-ring patterns of the deposit that are formed when colloidal suspensions are dried on a substrate. Using a standard model for the stick-slip motion of the contact line, the theory predicts (a) the multi-ring patterns are not observed at high evaporation rate, (b) the spacing between rings decreases with the decrease of the ring radius, and (c) the multi-ring pattern is taken over by a disk pattern near the center. These results are in qualitative agreement with existing experiments, and the predictions of the theory about how the evaporation rate, droplet radius and receding contact angle affects the pattern can be tested experimentally.