The act of missile riding can take place for several different reasons, depending on the needs of the character, and the circumstances that they find themselves in. The missile may be used for transportation from one location to another, to change its trajectory into order to avert disaster, or redirect it at an enemy.
There is also a distinction made as to what qualifies as a missile ride. Firstly, the object must be a missile, which is defined as a self projected projectile, powered by a rocket or jet propulsion. Therefore a missile range in size from a rocket from a rocket launcher, all the way up an ICBM. Other similar objects that may be ridden are not counted, such as falling bombs, torpedoes, or large shells or cannon balls. Additionally the act of riding can range in duration from several seconds of contact such as in Metal Gear Solid: The Twin Snakes, all the way up to the length of an entire stage, such as in Contra III: The Alien Wars.
Credit to GamesRadar and Mikel Reparaz who compiled many of the entries here.