Capillary open microsystems are attractive and increasingly used in biotechnology, biology, and diagnostics as they allow simple and reliable control of fluid flows. In contrast to closed microfluidic systems, however, two-phase capillary flows in open microfluidics have remained largely unexplored. In this work, we present the theoretical basis and experimental demonstration of a spontaneous capillary flow (SCF) of two-phase systems in open microchannels. Analytical results show that an immiscible plug placed in an open channel can never stop the SCF of a fluid in a uniform cross-section microchannel. Numerical investigations of the morphologies of immiscible plugs in a capillary flow reveal three different possible behaviors. Finally, the predicted behaviors of the plugs are demonstrated experimentally, revealing an effect of inertial forces on the plug behavior. A model for predicting plug behaviors in SCFs is proposed, enabling the design of open microfluidic droplet-based systems that are simple to fabricate and use. The open-channel approach to droplet-based microfluidics has the potential to enable applications in which each drop can be accessed at any time and any location with simple pipettes or other fluid dispensing systems.