These questions are mostly overflow from the Q&A section of the physics newsletter I produce for my old high school (The King Edmund School).
Pretty high! One estimate I found states that the Earth is hit by around 500 meteorites per year. But I think probably you were asking about things a little bigger than these pebbles!
Let's clear up a bit of terminology first: Asteroids are rocky (and a little metallic) body's that orbit the sun, generally bigger than a metre across, but smaller than a planet. Meteoroids are small fragments of Asteroids (or sometimes fragments of comets), generally between the size of a spec of dust and a metre across. A Meteor is the name given to a meteoroid that falls through the Earths atmosphere (creating the white streaks we call shooting stars), and a Meteorite is what's left of the meteor (if anything) when it reaches the Earths surface.
There's a very nice table on this Wikipedia page ( https://en.wikipedia.org/wiki/Impact_event ) showing the average frequency of asteroid impacts of a given size.
You can see that small asteroids (around 4 metres in size) hit the Earth roughly every 1.3 years. Asteroids of this size (and up to about 20 metres across) usually explode in an airburst, fully vaporizing before anything can hit the ground.
Asteroids of 250 metres in size hit the Earth roughly once every 59 thousand years. An asteroid this large would certainly be a 'city-killer', but wouldn't cause any real damage to the planet as a whole.
The last and only known example of a 'planet-killer' (10 kilometres + ) asteroid strike was the one that killed off the dinosaurs around 65 million years ago. Therefore the best estimate we can give for the frequency of these cataclysmic events is 'one every 65 million years', but with only a single data point, that is quite a high uncertainty. Fortunately, an objects this large headed for Earth would very likely be spotted in advance. Unfortunately... There is very little we could do about it.
I found this link very interesting, in describing the speculative long and short term effects of large asteroid strikes on the Earth, definitely check it out! ( http://www.vdrsyd.com/planet/climate.htm )
*work in progress*