Though most of the objects are too small to cause any sort of substantial damage, there are a few that are capable of causing the next major extinction. In order for an object to be considered a NEO, it must be within 1.3 AUs (or astronomical units) from the Sun. 1.3 AU is the same as about 93 million miles. The NEOs are objects that have been bumped by the gravity of other planets which let them get close to the Earths orbit.
One of the major groups of NEOs are meteoroids. The term meteor is actually used to describe the streak of visible light after its trip through the Earths orbit. One of the most famous craters, which is like a giant scar caused by a NEO hitting the Earth, is in Arizona. Meteor Crater, or Barringer Meteorite Crater as it is also known as, is a jarring reminder of what kind of damage a NEO can do upon impact. Most meteors are small enough that once they are pulled in by the Earths orbit and hit the atmosphere, they burn up and disintegrate before they ever get the chance to actually hit the Earths surface.
Another group of NEOs are asteroids. One of the largest asteroids that astronomers keep their eyes on is Apophis. This giant is due to hit the Earth in 2036. The size of Apophis is estimated to be a bit larger then the Rose Bowl, and if it were to hit the Earth would cause global damage. If it hits the ocean, the damage occurring from the huge tsunamis by themselves would be catastrophic.
Another class of objects that are visible to the naked eye are comets. When speaking of them as NEOs, then they are considered to be old comet nuclei whose perihelia are less then 1.3 AU from the Sun. One comet in particular that has been known through history is Halleys Comet. Also, the trail of cosmic dust, or tail of the comet can also be passed through by the Earth.
In conclusion, NASA is taking steps to try and diminish the risk of being hit by a NEO by continually watching and cataloging the orbits and behaviors of NEOs. What remedies that have been looked at so far to try and deal with the risk of being hit is to explode nuclear weapons near the object to try and change its course. Other considerations that have been looked at is sending high-speed ballistic missiles towards the object to make an impact, or to send a hovering spacecraft to pull the object into a different orbit, thereby allowing it to miss the Earth altogether.
The future for watching NEOs is strongly backed now more then ever before. Washington has allowed a $4 million dollar budget for listing potential and real threats to the Earth, and sent a new report to congress in March 2007. Considering the probability that the Earth will be hit again, as it has been hit in the past requires that the scientific community take heed of the risk, and not only be able to prepare the world for such a catastrophe, but be able to prevent it as well.