A meteoroid is a bit of debris from a comet or asteroid which is on collision course with the Earth. When the meteoroid burns up in the Earths atmosphere it forms a meteor (or shooting star). Most meteors come from particles which are about the size of a grain of sand. A grape sized particle would give an intense fireball, and objects which are bigger still can partly survive the descent: these are the meteorites we can find on Earth.
Plainly then the Earth does get hit by debris. Sometimes, quite big bits of debris - there are impact craters on Earth. A small fraction of asteroids have orbits which cross that of the Earth, so have some possibility of collision. A collision with a large asteroid was probably responsible for the extinction of the dinosaurs! Comets too are often on Earth crossing orbits, and one probably hit a remote region in Siberia called Tunguska. We know that a comet definitely hit Jupiter! This is the famous Shoemaker-Levy 9 impact of July 1994. It can happen.
But how frequently ? Not very often at all now. Yet looking at the numerous craters on the surface of the Moon, Mercury and (to a lesser extent) Mars means that they must have been very much more common in the past. Earth and Venus have atmospheres, so weathering and erosion soon wipe out the craters, whereas on the Moon, Mercury and Mars the old surface with its many craters is preserved. For much more on the planets see The Nine Planets Impacts would have been much more frequent in the early days of the Solar system, and then declined as most of the debris got swept up by collisions with the planets. So they are now rare, though clearly possible.
When a big meteorite hits a planet then the impact can be hard enough that some of the debris is able to escape from the gravitational field of the planet. These fragments can then wander around the solar system, and eventually impact onto another planet. Seems unlikely, but there are a few meteorite which have compositions which look much more like the Moon than the asteroids, and even fewer which seem to be from Mars. One of these caused great excitement with the claim that it showed evidence for life from Mars! A nice compilation of articles from the debate which followed is here. The jury is still out as to whether this is fossilised bacteria or crystaline structures. And if it is fossilised bacteria then could these have grown from the time the meteorite spent on Earth rather than on Mars?
Back to the night sky. Other things that can be see because they move are some of the many artificial satellites which orbit the Earth. We can see them only when they are lit by the Sun but we are in darkness. This means the few hours after sunset or the few hours before sunrise. The most obvious fact about them is that they move fast (and don't have flashing lights so they are not planes!) - they are generally in low Earth orbit which is ~90 minutes! Their brightness then depends on size and the biggest are Mir and the International Space Station. The Shuttle (when its up) is also easily visible, and predictions for times, positions and brightness (as seen from Durham) are here. But one can also see bright flashes from the Iridium communications satellites when their antennae reflect the Sun - these are called Iridium flashes. A list of predicted times to see these Iridium flashes from Durham is given here