Bloodlines acted a template of sorts, with new or altered weaknesses and disciplines tied in some way to their parent clan. The Melissidae, for example, are Ventrue who ape the style of insect colonies to turn dominated thralls into drone-like hordes acting under a telepathic hive-mind.
In line with their original mythos, another strong suit of Vampire is its hint of tragic romance. Cursed immortals trying and failing to imitate mortal life. The struggle between walking the high road without succumbing to the Beast. Even finding a willing blood donor creates complications, as the act of feeding is inimically harmful to humans, not to mention the addictive qualities of Vitae. Even White Wolf seized on this theme with a sourcebook of its own: Strange, Dead Love. Love can be a tricky subject for games, but if performed as a side tale for a character, or perhaps a strong moral anchor for one of the Damned, it can be a great generator of stories.
Let's face it; vampires are hot. Beyond that, they are dependent on mortals and their fellow Kindred for survival. The very set-up of the game encourages strong social bonds, even if said bonds are tinged with thorns. The following bloodlines are what I feel lend themselves best to romantic subplots.
Alucinor (Bloodlines: the Hidden, pg. 12): Dreams often bring portents of things to come and shine a light to one's true thoughts. These Mekhet know their power better than any others, with the power to divine, alter, and enter another's dreams or torpor.
Bron (Bloodlines: the Legendary, pg. 10): Nomadic Ventrue with ties to legends of the Holy Grail, the search for a 'true home' may bring them to find something more valuable than territorial holdings, that home is where the heart is.
Galloi (Bloodlines: the Legendary, pg. 51): Nosferatu who bathe in blood to overcome the weakness of their parent clan, maybe all they need is to find someone who can look past to the true beauty within.
Gulikan (Bloodlines: the Legendary, pg. 20): Originating among Daeva perfumers, their ability to imbue soaps, oils, and related paraphernalia with discipline powers grant a touch of supernatural sensuality. Their extreme fascination with the scent of a select few mortals is a good way to generate plot hooks and unlikely first meetings.
Khaibit (Onyx Path update): Once they were guardians fighting against a greater darkness, but now find themselves with a new purpose in fighting the Strix. Makes for a nice "dark superhero" bloodline.
Septimi (Ancient Bloodlines, pg. 89): Righteous Daeva who seek to protect humanity from evil influences via the manipulation of shadows, this bloodline makes for a good "guardian vampire" trope much like the Khaibit.
Spina (Invictus, pg. 173): Chivalric soldiers with a high emphasis on politeness and martial skill who serve the Invictus, such Daeva are the very model of the "vampire knight."
Taifa (Bloodlines: the Chosen, pg. 75): Gangrel who drape themselves in high art and scholarship, they stand proof that you don't need to be a Daeva or Ventrue to appreciate the finer things in life.
Toreador (Vampire the Requiem, pg. 246): Daeva obsessed with all kinds of art yet unable to create such works themselves, this bloodline's the perfect match (and muse) for a partner of the creative variety.