In the Femininity in Games episode of the Moving Pixels podcast, it was mentioned that very few games with female lead characters allow the player to pursue a romance. I guess this is because the gamers are still predominantly male.
I've played some male-centric games that feature romance, such as Riviera: The Promised Land, Sakura Wars: So Long My Love, Prince of Persia: The Sands of Time, and a few Final Fantasy and Persona games. I've noticed that they portray romance much differently from romantic movies aimed at women, such as Notting Hill and The Notebook.
In romantic films, the man and woman usually have a rocky path toward becoming a serious couple. There will be initial rejection, foot-stomping, door-slamming, crying, and misunderstandings. It all works out in the end, but the two may not be truly together until the movie's parting shot. So women enjoy a romance filled with uncertainty, turbulence, and even long periods of isolation for both the male and female leads.
In games that feature romance, the romance is portayed in almost the opposite fashion. It builds slowly but surely. As the chapters pass, the male and female characters will have more frequent, more meaningful conversations. They usually stick together and don't experience a major falling-out. Their relationship is made stronger by the dangers they face in the game, and their mutual assistance leads to mutual emotional dependence. So, if men are the main audience for games, then men enjoy a journey of stable, dependable togetherness.
I believe men enjoy romance in their entertainment as much as women, but games are better than films in portraying romances that men enjoy.
There is a similarity between romance movies and the "harem romances" of certain Japanese roleplaying games such as the aforementioned Riviera and Sakura Wars. In both, the lead character is faced with a difficult choice of suitors. She or he may bounce from one romantic interest to another, not sure who to be with. In the end, though, the lead makes a choice, and the movie or game rejoices in it, celebrating it as the best choice.