Akira (1988)

Akira is one of the most important animated films ever made, and the hand-drawn animation still looks incredible. The science is weak - the story is driven by psychic powers, which is closer to fantasy than science fiction. But the world around the story feels uncomfortably real: secret military experiments with no oversight, a city rebuilt on the ruins of a disaster, and people who no longer trust anyone in charge. You can see its influence in so much of the sci-fi that came after it. If you've never seen it, it's worth watching for that alone.