The Stranger (also sometimes translated to
The Outsider) immediately made me think of the English translation of the title for the novel
L'Étranger by
Albert Camus. A definite classic (they made us read it in school back in my day, anyway). There is also a famous movie called
The Stranger with Orson Wells, which you mentioned (not based on the same story).
A quick perusal of
Amazon reveals that there are other books by this title too, the most recent being
The Stranger by Amelia Lackberg (2014), and
The Stranger by Harlan Coben (coming out in 2015).
So maybe this answers your question. Yes, it's possible for books to have duplicate titles, even of classics, though this might work better with a somewhat "generic" sounding title like "The Stranger" than it would with a really standout name. Also, it might be a good idea to avoid having the same title as a well-known book in your own genre. Writing a fantasy novel (for instance) called
Lord of the Rings, or
The Wheel of Time might backfire, not for copyright infringement, but because it would confuse potential readers.
As others have said, if you are going for trade publishing, the publisher will likely weigh in on the title. I don't have exact figures for how many writers get their submission title changed, but the practice is fairly common. It may vary with genre. I've met writers who say their publisher always takes the title they've chosen, and others who say their publisher always changes it.
May be a function of how good one is at picking interesting titles that grab the interest of the target audience.