Given the nature of explosive volcanic eruptions here on Earth and the important roles of dissolved gases and plate tectonics, what might you expect of volcanoes erupting on other planets?
Well, I would expect any planet with no plate tectonics to have little to no volcanic eruptions. If there is no mantel, then there would be no liquid rock for the planet to eject in the first place. In addition, the presence of volcanoes on a planet would suggest a mantel and possible plate tectonics.
Dissolved gasses in the magma are released as volcanoes erupt. On earth, these gasses are commonly water vapor, carbon dioxide, sulfur dioxide, sulfuric acid, and hydrogen halides like HF, HCl, and HBr. A strongly volcanic planet would have an atmosphere of similar composition; consider, for example, Venus. Venus is the most volcanic planet in the solar system, with almost 90% of the surface being basalt rock, or freshly cooled lava. The atmosphere of Venus, in comparison, is primarily carbon dioxide with trace sulfur dioxide--an almost perfect match.