It depends on how the moon is cleaved, but most cases are the same. If escape velocity isn't reached they will just reform and we might get negligible space debris from the collision. The moon might also reform in a position slightly closer to us than before. It would speed up the time of our days (negligibly).
If the two halves of the moon do reach their own escape velocity, the first half would speed up, increase its distance from earth, and then remain in its new irregular elliptical orbit. The other half would slow down and either spiral toward earth and destroy all life or begin an elliptical orbit with a minor radius dangerously close to Earth. In other words, if we survive this option, we'd likely have two moons.
If the latter happens, tides would be changed, the angle of the axis of the earth could change, and/or we could be hit by the slower half of the moon and all die.
This post was edited by EndlessSky on Jan 11 2012 09:35pm