All capacitors come with a voltage rating. That is the recommended maximum operating voltage for the capacitor. In general, the capacitance of a capacitor of a given size will vary roughly inversely as the voltage rating. So you might find a capacitor of 10µF at 150V at about the same size as a 100µF at 15V. The protection of the capacitor comes from the design of the circuit. The designer will know the voltage levels the capacitor will be working at. The designer will pick a capacitor of high enough voltage rating so that its maximum voltage will not be exceeded. Usually, the rating used is higher than the known maximum voltage in the circuit in order to provide a safety factor. However, the rating itself includes some safety factor. A capacitor rated at 100v will not suddenly blow up at 110V.
Different dielectrics have different breakdown field strengths, with glass, ceramic and mica being the strongest, and the thin dielectric coating on an electrolytic capacitors being the weakest.