12 Monkeys (1995)

This is one of the few time travel films that plays fair with its own rules. The hero is sent back from a future where a virus has wiped out most of humanity, but he can't change what happened - he can only gather information. Everything he does was always part of history. That makes it far more logical than most time travel stories (compare it with the Terminator films!). Time travel itself is still impossible, which keeps the science score down, but the pandemic story felt unsettling back then and is much more unsettling now. It's confusing the first time you watch it, and it's better the second time.