There are many movies and TV episodes in which a character "crosses his own timeline", sometimes even meeting his past or future self (e.g. The Day of the Doctor). Technically, I should say meeting his past self and meeting his future self, I suppose, since this is actually what happens.
When they supposedly alter their own future resulting in their never having travelled in time (as in Back to The Future or Looper), or narrowly avoid doing so, this is known as the "grandfather paradox".
How are we, the audience, supposed to make sense of this, if we actually think it through logically?
If you perform an action which has an effect that you never survived or were never ever born, then how did you travel in time in the first place? (Although it's not really "in the first place", if you travelled backwards in time...)
I know that there is some quantum mechanics theory relevant to this but the average cinema-goer doesn't know about all that stuff, surely...