12 Monkeys / La Jetée

In this cyclical story - the former being Terry Gilliam's feature adaptation of the latter short - a man is sent back in time in order to prevent the outbreak of a virus / stop World War III from happening. In both versions of the story, the protagonist's vague memories of a shooting at an airport play a vital role in his mental ability to connect to the past. Turns out, those memories are a bit bleaker than we're initially led to believe - it was himself that he watched get shot as a young boy. To make matters worse, 12 Monkeys plays up the idea that its protagonist may be insane and making the whole thing up, a theory amplified by the appearance of one of the future scientists in the final moments of the film.