It really depends on the superhero in question. Batman movies for instance need to use the romantic angle in strict moderation. Wayne is a lady's man, no doubt about that... but when it gets down to the story itself, the Batman comics have never been based off of the 'villain captures girlfriend, uses her to blackmail our hero' formula. Nor have they been about 'I'm losing my sense of responsibility to my mission because I'm so in love with (Vickie Vale, Selina Kyle)' Has he been tempted with notions of retiring from being a vigilante and pursuing someone he is interested in? Of course. But at the end of the day, Batman knows he must be Batman, and cannot allow genuine romance to fog up his self-given mission. So far this fact has been respected by writers of the comics and movies. Tim Burton notably did a terrific job at conveying it.
Now if we're talking about other heroes... Superman for instance. SR really took the romance to the extent of: I have feelings so strong that I'm going to forget my morals and spy on my ex even though she has already set up a new life and family after I disappeared for five years. Superman is allowed to be in love, he's allowed to have passionate feelings, but when a hero such as that forgets who they are in the face of those passions, then that is taking it too far.
Spider-Man? His character was conceived on the premise of how a younger man can juggle school, girlfriends, and a hero life. So it would be relatively hard to take romance to ridiculous extents when it comes to Spidey.