Spanish astronomers recently calculated that, on next February 15, approaching asteroid 2012 DA14 will pass within 17,000 miles of the Earth – potentially closer than many satellites. redOrbit explains what would happen if the asteroid did hit:
The [University of Central Florida] said that the impact of an asteroid approximately the size of DA14 would have destructive power equivalent of “an atomic bomb”, while a larger one would be "catastrophic."
According to the UCF, NASA has identified more than 4,700 asteroids that are "potential threats to Earth, some as big as 16 football fields." Meanwhile, an MIT graduate student has a plan for deflecting asteroids:
Sung Wook Paek, a graduate student in MIT’s Department of Aeronautics and Astronautics, says if timed just right, pellets full of paint powder, launched in two rounds from a spacecraft at relatively close distance, would cover the front and back of an asteroid, more than doubling its reflectivity, or albedo. The initial force from the pellets would bump an asteroid off course; over time, the sun’s photons would deflect the asteroid even more.
For a better sense of the potential damage of an asteroid collision, Purdue University's Impact Earth! is a handy simulation tool. Previous Dish coverage on the axing of NASA's asteroid research here.