It's a question wether you want people to recall or recongnize movies.
If you want them to recall, there's no reason to show anything fancy, an empty searchbox will do.
If you want them to recognize, you should list some movies first.
Use a kind of autocomplete which is used in e-mail sending, facebook message sending and tagging (like, at this question). It's called multiple value autocomplete, "facebook-like autocomplete" and so on. Use the image of the movie (DVD cover or such) as an avatar.
Bear in mind, that a portion of users aren't likely to have a decisive answer to that. Some people have no decisive answer to such question, and say "that's one of my favourite film too!" when it enters the conversation, or when they've seen it recently.
Sort the list by release year. Ask them when were they born and start the list around when they were about 10-12 years old, and show about 10 years. I think that films which we have seen at a more younger age have more lasting impression on us than the films we see later, but this hypotheses needs to be tested.
Of course, you can meet a film which makes a great impression on you years after that, and nothing prevents you to see films which were made long ago and still have a big impression on you - how many Star Wars fans were born after 1977?
So there's no decisive answer to your UI question I guess, just as there's no decisive answer for the question: "What is your favourite movie?" to me.