I've got three for you. None of these are traditional romance movies either.
1 - Casablanca - While Rick and Ilsa do not end up together, the relationship between them is superb and the twists and turns endless.
2 - Life is Beautiful - The theme of the film is quite dark (the holocaust) however the relationship between the main characters is beautiful.
3 - Garden State - A wonderfully quirky film and the central romance between Zach Braff and Natalie Portman is great.
Not only are these three of the most romantic films, but also three of the best.