Final answer:
Methane (CH4) plays the same role on Titan as water does on Earth, existing as gas, liquid, and solid.
Step-by-step explanation:
The compound that plays the same role on Titan as water does on Earth (existing as gas, liquid, and solid) is methane (CH4). Methane exists on Titan as a gas in its atmosphere, forms lakes and rivers of liquid methane on its surface, and can freeze into solids. This is similar to how water exists on Earth as a gas in the atmosphere, forms bodies of liquid water, and can freeze into ice. Other compounds mentioned, such as carbon dioxide, ammonia, hydrogen cyanide, and propane, do not have the same properties of existing as gas, liquid, and solid across the conditions found on Titan.