Her gets AI right in a way that most movies don't. If you're willing to buy into the movie's premise that an AI that perfectly communicates in human language and has human-like desires is possible, the movie explores the very likely relationships that will form between those AI persons and the humans that associate with them. It declines to address the specifics, but it relies on early emotional appeal to get the audience on board, and it works. The few "Hey, wait a minute..." moments that I had were almost all after I left the theater and thought about it.
Which is not to say that I found myself getting resentful after the movie is over. I am easily able to see past the few omissions that I noted in favor of a tone of the movie that feels very real. This is ordinary (well, futuristic wealthy Los Angeleno ordinary) people interacting with a wildly new possibility and integrating it into their lives. This is in marked counterpoint to the breathless malevolence of AIs 2001: A Space Oddyssey or Terminator, or the banal non-personalities of AIs in Star Trek or Moon. If we truly create a computer personality that mimics a human, then ipso facto it will behave like a human. Her understands this and get it right.
Spike Jonze has crafted a script that is philosophical and convincing. It's simultaneously about interpersonal connection and alienation, and there's a lot more to say here than merely a bit of dithering on what AIs will mean, but also what our increasingly information-oriented and automated lifestyle means. It's the best of sci-fi: it tells us a future that, in turn, tells us about our present.