The wetting behavior of ring-shaped (or annular) surface domains is studied both experimentally and theoretically. The ring-shaped domains are lyophilic and embedded in a lyophobic substrate. Liquid droplets deposited on these domains can attain a variety of morphologies depending on the liquid volume and on the dimensions of the ringlike surface domains. In the experiments, the liquid volume is changed in a controlled manner by varying the temperature of the sample. Such a volume change leads to a characteristic sequence of droplet shapes and to morphological wetting transitions between these shapes. The experimental observations are in good agreement with analytical and numerical calculations based on the minimization of the interfacial free energy. Small droplets form ringlike liquid channels (or filaments) that are confined to the ring-shaped domains and do not spread onto the lyophobic disks enclosed by these rings. As one increases the volume of the droplets, one finds two different morphologies depending on the width of the ring-shaped domains. For narrow rings, the droplets form nonaxisymmetric liquid channels with a pronounced bulge. For broad rings, the droplets form axisymmetric caps that cover both the lyophilic rings and the lyophobic disks.