I almost never do this.
The only reason I can think of to relocate your capital is to make it more centralized. Just like in Civ 3, cities suffer a penalty (I forget exactly what the penalty is) the further they are from the capital. So if your capital is on the far end of a large empire, the cities on the opposite side of the empire will never be as productive as the ones nearest the capital. In a situation like this, you might want to move the capital into the middle somewhere and even out the benefits.
The Forbidden Palace Wonder used to provide you with a "second" capital which had the same effect as the main one in terms of lowering corruption. I'm not sure if it still has the same effect in Civ IV. If so, then moving your palace is even less worth it, since in the above example you could build the Forbidden Palace on the other end of your empire.