It's especially interesting that "Planet of the Apes" was released a few months before "2001: A Space Odyssey", as they both look at the same question: what will become of humanity (and how did we originate)? Obviously, the really famous line is Charlton Heston's snap at his captors, and the really famous scene is the end - which I won't tell here for fear of spoiling the whole movie. And what an impressive movie it is! Unfortunately, I can't say the same for Tim Burton's remake. "POTA" should never have been remade. So, for a cinematic treat, stick to this one and avoid the remake.
One more thing is that some people have pointed out that the portrayals of the simians were kinda racist. The blond, cultured orangutans are the nobles; the dark-haired, mildly nervous chimpanzees are the scientists; and the dark-skinned, incompetent gorillas are the police. Oh well. It's still a good movie.