A number of papers on the risks, potential damages from impacts, and
ways to mitigate the danger is at
<URL:http://www.llnl.gov/planetary/>.

Our ability to prevent impacts depends upon several things, the size
of the object, its orbit, and the amount of time until impact.
Generally speaking, the more time the better.  It is perhaps
counter-intuitive, but we could mount the best defense against objects
in orbits similar to that of Earth.  Such an object would pass close
to Earth several times, giving us many chances to discover it,
calculate an extremely accurate orbit, and launch one or more missions
to it.  We might have decades or even centuries to plan.  Conversely,
a comet on an impact course might be discovered only a month or so
away from impact, giving us little or no time to act.

The optimum approach to avoiding an impact is to discover an object
well before impact and gently nudge it.  If discovered long enough
before impact, only small nudges are sufficient to change the object's
orbit so that it will no longer strike Earth.  There are a number of
strategies to nudge an asteroid including landing a rocket engine on
the asteroid or vaporizing a small portion of it with a laser or
stand-off nuclear blast or reflected, concentrated sunlight.

Popular depictions of laser beams or nuclear weapons being used to
blast asteroids into pieces are usually unrealistic; moreover, if
actually used, such "solutions" would probably make the situation
worse.  First, it is unlikely that the firepower exists to blow apart,
say, a 5 km asteroid.  Second, even if we could blow apart an
asteroid, most of the pieces would stay on essentially the same orbit,
i.e., on target to hit the Earth.  A rain of 1000 100-m--sized objects
could still cause considerable damage.