If a large asteroid headed for the Earth were noticed in time, say 10 years ahead, how could we safely get rid of it?

Speculation on this possibility was first proposed by science fiction writers—a good example is The Big Eye by Max Simon Ehrlich (1950). Since the development of rocket technology (say, since WWII), several scenarios have been proposed. At first, it was though the such a meteor could be met with an explosive rocket that would break it into tiny pieces—this possibility was discarded when scientists found that the pieces would pose as devastating an effect as the chunk itself.  More recently, with the refinement of satellites and planet/moon exploratory robots, a proposal has been voiced to land a strong device (rockets or explosives) onto the surface of the asteroid that would simply change its course slightly but enough to miss the Earth.  The whole subject is fueled by fear-based "end-of-the-world" theorists.