The Kessler Effect
The movie: The Russians randomly decide to chuck a missile at one of their satellites, which causes generates a cascading chain of debris. Traveling at incomprehensible speeds, the debris acts like shrapnel, tearing apart everything in its path, which in turn creates more space-bullets.
Real life: What happens in the movie is called the Kessler effect, and it's a real fear for space scientists worldwide. For that reason, there are a number of safeguards in place to prevent such a disastrous event. The Hubble and the ISS would have to be on intersecting orbits with the debris field — this kind of thing is scrupulously avoided in outer space precisely because the Kessler effect has such deadly ramifications.