A first quick thought that comes to mind is Gone With the Wind, which may sound odd to some people! That movie with Rhett and Scarlett as well as Ashley and Melanie, has some great romantic parts to it! It helps tie the whole movie together, and made me want to read the follow up book, Scarlett where they get to pursue that relationship further. So Clark Gable and Vivien Leigh were great in that movie. Its a longer movie of course, so there is more time to really build up the story.
In general, I like movies that have side love stories like that, that aren't really the focus of the movie, but a natural part of the story. Its kind of how life is sometimes too. Good question,