We have developed a radio-frequency-powered non-equilibrium argon gas discharge consisting of two parallel electrodes, with at least one being covered with a thin dielectric layer. The atmospheric discharges that take place in such an experimental device are of different types, depending on the experimental conditions, particularly on the product pd of gas pressure p and discharge width d. Spatiotemporal pattern formations and microdischarge phenomena occurring in this atmospheric plasma discharge have been studied by using a high-resolution video camera. In particular, we observe moving fingerlike structures, occurring as the argon plasma expands radially across the electrodes, which are indicative of fluidlike behavior. Other spatiotemporal phenomena include traveling localized and starlike discharges. All of the observed phenomena can be controlled by varying the RF input power, gas flow, and discharge gap size.