I think the definative book on the subject is 'Lucifer's Hammer' I think it's by Larry Niven and Jerry Pournell.
It's a full-blown hard-science (i.e. it makes sense) account of a big-one hitting Earth.
Now, statistics are a dangerous thing. About half the people in the USA are under average intelligence. Get it?
Also, aeroplanes crash on a more regular basis than asteroids, but asteroids have a higher body count. Thus, statistically, you're more likely to die from an asteroid falling on your head than in a plane.
However, it is quite unlikely we'll have even a close encounter with anything in any of our lifetimes, or our children's, or theirs.
Or it could happen tomorrow.
Given the liklihood I will not be patenting the Asteroid-Proof Umbrella just yet.
But it has happened before; they reckon the crater of one is, basically speaking the Gult of Mexico. Likewise Hudson Bay. Those are BIG ones. Little ones, like Meteor Crater, well, if you're near by bad luck, but it ain't the e'ot-waw-ki (a Hawaiian word meaning 'end-of-the-world-as-we-know-it').
Depending on the size of the asteroid, it could be back-to-the-stone age, or back to Christian Fundamentalism, er, I mean monocellular life.
The plot of 'Lucifer's Hammer' is cute, as it's enough destruction to have something to start again, but not too much, religious crazies eating people, but the good guys winning through in this rather appealing frontier atmos.
As for prevention, well, given time you could land on a potential Earth-hitter and plant nukes. Or try to mount thrusters on it to give enough delta-vee to miss the Earth. It would be one way to get rid of ICBM's; anything with escape velocity that goes 'bang' would be called into play if all else fails. But at about seven tonnes a cubed meter, a really big one would really take some dissuading if it was on an impact course.
But, if we had enough warning, the most practical thing to do is stockpile food and head for high-ground, and hope as the telemetry gets clearer you haven't chosen high-ground in the wrong hemisphere!
Keep on rocking in the free world...