That would depend entirely on HOW it left orbit. If it was part of some cosmic billiard game, there could be lots of rubble drifting around, and since the Earth is the biggest gravitational field in the area we would be rained on by millions of chunks of rock, day and night for thousands of years. This could be lethal for the biosphere. If the Moon just suddenly packed its bags and 'left' , the Earth would no longer feel the lunar tidal field and the ocean tides would loose about 1/2 of their height just like that. The other half is, of course, provided by the Sun. There might be some perturbation to the length of the day depending on the exact dynamics involved, also the precession of the equinoxes would change since the lunar-component of the torque which is producing it would vanish. Then there would only be the precession caused by the Sun, I believe, although I am not an expert on this entire business.