We report observations of spontaneous formation of micrometer-sized water droplets within micrometer-thick films of a range of different oils (isotropic and nematic 4-cyano-4'-pentylbiphenyl (5CB) and silicone, olive and corn oil) that are supported on glass substrates treated with octadecyltrichlorosilane (OTS) and immersed under water. Confocal imaging was used to determine that the water droplets nucleate and grow at the interface between the oils and OTS-treated glass with a contact angle of similar to 130 degrees. A simple thermodynamic model based on macroscopic interfacial energetic arguments consistent with the contact angle of 130, however, fails to account for the spontaneous formation of the water droplets. zeta-potential measurements performed with OTS-treated glass (-59.0 +/- 16.4 mV) and hydrophobic monolayers formed on gold films (2.0 +/- 0.7 mV), when combined with the observed absence of droplet formation under films of oil supported on the latter surfaces, suggest that the charge of the oil-solid interface promotes partitioning of water to the interfacial region. The hydrophobic nature of the OTS-treated glass promotes dewetting of water accumulated in the interfacial region into droplets (a thin film of water is seen to form on bare glass). The inhibitory effect on droplet formation of both salt (NaCl) and sucrose (0.1-500 mM) added to the aqueous phase was similar, indicating that both solutes lower the chemical potential of the bulk water (osmotic effect) sufficiently to prevent partitioning of the water to the interface between the oil and supporting substrates. These results suggest that charged, hydrophobic surfaces can provide routes to spontaneous formation of surface-supported, water-in-oil emulsions.