The consensus among scientists today is that the earth's continents have drifted apart over the ages due to the spreading of the sea floor caused by the introduction into the crust of new rock from deep in the earth's mantle. This new rock, the theory goes, is exuded through crevices in the mid-ocean ridges and pushes the continents away from each other. The continents then slide under each other along contact faults in a process called subduction. This returns rock back to the mantle where it's melted.
There is a minority view, however, which holds that continental drift is not a result of sea-floor spreading and subduction but rather is caused by an expanding globe. According to this theory (see video) the earth is inflating like a balloon, and it's this expansion which pushes the tectonic plates(continents)apart. The earth's crust was originally a solid shell, the story goes, and over vast time the planet grew in size forcing the crust to fracture and spread. There are http://en.wikipedia.org/wiki/Expanding_earth_theory various hypotheses as to the causes of the expansion, but that it happened the narrator of the video, Neal Adams, is quite convinced:
Wait until the global warming people here about this. They'll be hurling themselves off of bridges.
HT: Jonah @ NRORLC