Direction a tornado tracks in the Northern Hemisphere...?

If I am correct, most tornadoes formed in the U.S. will move to the south or east, and occasionally to the north. I know that tornadoes are also generally unpredictable, however, why is it so rare for a tornado to move from the east toward the west across very large (relatively speaking) distances? And what would cause one to move to the west? Does it all depend on the direction the supercell is moving, or can the twister itself move independently of the cell once it has formed?