While some may scoff, I'd say that
Superman Returns does an amazing job of subtly, visually conveying that ellusive, inarticulate ache of being in love with someone who doesn't love you back. All of the small stolen glances when she's not looking. It's stuff like this that makes Bryan Singer a master filmmaker.
A few other action movies with love stories that absolutely melt me...
Batman Returns is probably my favorite. I just rewatched it today. The desperate longing between Bruce Wayne & Selina Kyle is so palpable. "He makes me the way I hope I really am." Beyond the epic, doomed nature of their love, they also have some fun romantic banter.
"I'm listed."
"I'm tempted."
"I'm working."
"I'm leaving."
Similarly,
Daredevil (particulary in the Theatrical Cut) provides a great love story between 2 inherently broken people who are absolutely surprised to find themselves made whole when they find each other.
The Kyle Reese/Sarah Connor romance in
The Terminator includes probably the greatest, most beautiful sex scene in cinema history.
As for more obvious romances...
While You Were Sleeping is a great one. This will likely always be Sandra Bullock's best entry in the romantic comedy genre.
Amidst all the raunchy nudity,
Forgetting Sarah Marshall has a very credible romance at its heart. They're just 2 very good people and you can't help but root for them. Also, they're people I would expect to meet in real life, unlike most objects of romantic comedy.
My favorite coming of age romance is
Rushmore. I defy anyone not to fall in love with Olivia Williams in this film. She absolutely breaks my heart when we see that tear run down her face as she says, "One dead fingernail."
Keeping the Faith is good. A comedy about a priest and a rabbi who both fall in love with their old friend from childhood, Anna.
Honestly, I hated this movie. There's just something very unseemly about the whole thing. I also don't see Anna having any chemistry with either lead. And why is the Jewish congregation so concerned about the rabbi dating a gentile and yet not concerned at all with the fact that he slept with a woman out of wedlock?