The answer for today is probably no. While the moon shows significant evidence of asteroid and meteoroid impact from the past, the current thinking is that all the asteroid material has been pretty much swept up and isolated to places like the Oort cloud. The moon has close to 300,000 different craters that bear witness to the collisions that have occured in its existence. Due to the fact there is little to no atmosphere on the moon, most asteroids and meteoroids from the past have made it to the moons surface with no problem. Earth has a significantly thick atmosphere which causes most meteoroids to burn before they make it to the surface. Asteroids being composed of larger masses of material, have a better chance of making it to the surface. There are several examples of collisions that might have been made by asteroid-like bodies, most recently in Siberia, Russia.
One more thing, wouldn't an asteroid hitting and destroying the moon. be as bad as one hitting the earth?
I should refrase it. On the near earth objects daily report it shows some days having 5 near earth asteroids pass. How many of those are hitting the moon?