Here are a few things to consider when making a vampire character. There are many other that are probably not listed here, so use this as a starting off point These aspects should be considered as well as all those other character points (backstory, profession, etc.). Remember, the idea is to make your vampire unique!
The Vampire Rules
What is your theory on vampires? Can they go out in the light? Are they allowed to make other vampires? Are they allowed to kill their victims? Building a vampire world before you set down to build your vampire character is crucial. You want to make sure that your particular vampire follows the rules of your world (or if s/he doesn’t, be able to explain why the rule doesn’t apply!
View of Vampirism
Is your vampire thrilled by the notion of his existence? Does she despise herself when looks in the vampires? Is she eager to bring others over to her nocturnal lifestyle?
Does your vampire have trouble controlling his or her urges? Does she feed on people? Does she feed on animals? Does the character hurt victims? Or is the experience of being fed on sensual?
Vampires, in many screen and story incarnations, are no long constrained by attraction to one gender. There are many vampires who have loved both men and women. This makes vampires even more appealing as a source of romantic friction or a love interest.
Vampires can live incredibly long lives, if not forever. Is your vampire ancient (say Roman or Egyptian) and has centuries of experience to draw on in modern life? Was s/he made recently and is familiar with the modern world? Was your vampire made during a time of war and takes a dim view of humanity?
Was your vampire made in the bloom of his/her youth? Is s/he a bit older? Is s/he a child and will always be a child? At what point in life a vampire was made determines his or her view on immortality and the human experience.
Does your vampire have long nails? This aspect of a vampire comes from the notion that hair/nails grow after death (or appear to grow). So, consequently, some vampires have very long nails, even if they are male.
Are the vampire’s fangs omnipresent? Do they elongate like werewolf canine teeth? Do they flip out like in True Blood? Can the vampire control their fangs or do they come out when s/he is especially hungry (or lusty!) The fangs are a very important symbol, so put some thought into it!
In closing….make sure that your vampire is well-formed (not just a human with fangs), different from other genre vampires, and captures the imagination!