I agree with nfw and Archon_Wing but would add a couple of things.
Missiles can be used to extend the effective range of the missile cruiser. For example, recently, I was trying to intercept an enemy destroyer that was heading towards one of my cities' fish resource. The aircraft from the city bombed it down to 50% strength but the intercepting fleet did not have quite enough movement factors to actually attack the destroyer. They were able to get to three tiles from it, two missiles fired from the cruiser finished off the destroyer.
They are good for taking out improvements that are within four tiles of the coast. I have used them to destroy oil wells and uranium mines, as well as forts that produce those resources, thus preventing the enemy from producing ships, planes, and tanks. Planes can do so as well but in my experience fighters fail much more often than missiles. Bombers are best for this but you don't always have a fort or city within range to base one at.
The down side to keep in mind is that every missile used is gone. So, the hammers used to build it are gone as well, unlike other military units which, if used with proper care, can survive the encounter. I always weigh whether the exchange is worth it, except when I have a huge empire producing more military than I can figure out how to use. Also, although I am not certain on this, I think that when you destroy an enemy unit with a missile, you don't get any GG points, unlike when you use a ship or ground unit. This last is simply based on watching what happens to my GG point display using BUG.