Several possibilities:
A causality loop: You kill your grandfather, preventing your father/mother from being born, preventing you from being born, which prevents you from going back in time and killing your grandfather, which prevents you from ceasing to exist, which enables you to go back in time where you kill your grandfather. Beyond that loop, the time-line progresses normally.
A branch: The death of your grandfather results in the creation of two separate but parallel time-lines, the one from which you came from and the one where your grandfather is dead. Both time-lines progress normally.
Predestination paradox:
Quote:
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Originally Posted by Tam Li Hua
...the wound doesn't kill or seriously injure your grandpa, and it ends up being the wound he told you about when you were a little kid.
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The time-line continues to progress normally.
Temporal balloon goes pop: The very act of traveling through time tears the space-time continuum, resulting in the annihilation of past, present, and future.