Notable Examples: Love at First Bite (1979), The Lost Boys (1987), Queen of the Damned (2001), Twilight (2008)
Above all else, the vampire-human relationship has been fetishised beyond genre. The days of vampires using humans as a source of food until angry villagers plunge a stake through their undead hearts are gone. Now we get to watch vampires really love. Sometimes we miss the old days.
Still, vampires have always had romantic potential—it's in their lore. They're known to be good looking in order to attract mates/dinner. They can kinda/sorta hypnotize a person. They only come out at night because day dates are friend zone material. And, we guess, there's something romantic about spending eternity with someone else (assuming your vampy lover turns you). And—even bigger guess right now—some people might find it romantic that someone loves them so much they want to drink their blood. Angelina Jolie?
Twilight's appeal isn't new. As long as there have been vampire flicks, there have been humans seduced by vampires, and vampires falling in love with their food.