I know it doesn't really fit into the archetypal "romance" genre, but it's still a really beautiful-if tragic-motion picture.
I'm not much of a movie buff, but that was the one picture that sprung to mind when you asked that question.
But there are so many captivating romances in literature that I could talk about.
Some of my favorites:
The ongoing love affair between Scarlett O'Hara and Rhett Butler.
I even enjoyed reading the sequel-Scarlett-written by Alexandria Ripley, which I think gets a bad rap by literary critics.
Also, the romance between Marius and Cosette, which happens to occur in one of my favorite novels, Les Miserables.
Finally, the love between Jane Eyre and Rochester, which I think is so memorable for some of the same reasons that Rhett and Scarlett's affair remains so powerful years after "Gone With The Wind" was published.