Predestination paradoxA predestination paradox, also called a causal loop, is a paradox of time travel that is often used as a convention in science fiction. Essentially, since it is impossible to experiment with time travel, a number of explanations have been given in various works of literature and film for various circumstances that arise. The idea is that when one travels back in time, one may influence events while in the past. These interactions have a direct effect, usually bad for purposes of the plot, on the future and the time travellor. The famous example is of a person going back and killing his own parents before he is born, forcing himself to not exist. In many cases, the causal loop has been used as a means in and of itself to provide a plot, and sometimes time travel is not even directly involved.
Suppose a man travels back in time and impregnates his great-great grandmother. The grandmother would thus give birth to one of the man's great grandparents, who would then give birth to his grandmother or father, who would then be able to give birth to one of the man's parents, and finally to the man himself. As a result, the man's very existence would be pre-determined by his time traveling adventure, and therein lies the paradox.
The classic example is shown in the movie Back to the Future. In it, Marty McFly (played by Michael J. Fox), travels back from the year 1985 to 1955, and prevents his parents from falling in love. This has the effect of causing himself to not exist. By the end of the movie, of course, he gets them back together and is able to save himself. The next two sequels deal with variations on the theme.
The Predestination paradox is very closely related to the Grandfather paradox. Please see that page for a more detailed analysis of possible genetic paradoxes posed by time travel.