Near-Earth Objects
Large near-Earth Objects (NEOs), greater than about 50 metres in size, can pose a threat to the Earth. NEOs less than 50 metres, depending on their size, composition and structure either explode or burn up in the atmosphere. Sometimes fragments of the original survive and fall to the surface as meteorites. The US and other nations have search programs to catalogue and tag any particular threatening asteroids.

A map of known asteroids in the inner Solar System. The red and green dots are Potentially Hazardous Asteroids (PHAs). Click on image to view larger version. (Image: Armagh Observatory)
A Potentially Hazardous Asteroid (PHA) is one that comes within 0.05 AU (several times the distance between the Earth and the Moon) and has an absolute magnitude of 22 (this translates to a size of about 150 metres). A database of these are currently updated and published on the web for astronomers and others to access.
The reason for the word 'Potential' before 'Hazardous' in PHA is that there will always be some uncertainty in measuring the orbital track of the asteroid and therefore predictions of its location in the future will also be uncertain. However many measurements of the asteroid along its path can improve the uncertainty. Eventually the PHA will become just an A (asteroid) or it will become a HA (hazardous asteroid).
Currently we know the wherabouts of most of the NEOs larger than one kilometre in size (there are roughly 1000 NEOs greater than 1 km in size). These large NEOs could cause devastation on a global scale due to the amount of dust and debris kicked up from the impact explosion. The effect on the climate could be similar to a nuclear winter scenario where temperatures are depressed and crops fail.
It is important to remember there are many many small objects (less than 1 km in size) out there that we haven't detected and could cause local devestation on Earth. However there are plans to catalogue NEOs down to 150 metres in size.
None of the NEOs discovered so far are predicted to hit the Earth with any absolute certainty but there are many hundreds of PHAs out there that need their orbits properly constraining and may one day turn out to be really dangerous.
If an NEO is found to be on a collision course with Earth we could probably push it out of the way using one of the many methods and technologies studied by scientists and engineers.