Creatures of myth, legend and fantasy tend to hold with them a lot of different interpretations, which means when you dream about anything supernatural there isn't a fixed universal meaning behind it. So what are the various connotations when it comes to the humble vampire?
If you consider vampires to be sexual figures (the likes of Lestat or Edward Cullen), you may be secretly longing for a new romantic adventure, or else imagining meeting a tall, dark, handsome stranger. Vampires feed off humans for survival, so perhaps you are yearning to be needed or desired sexually.
If, on the other hand, the vampire is more the Nosferatu type, this could mean that there is someone in your life who isn't doing you any good. Perhaps they are figuratively sucking out all the pleasure in life, or else burdening their negativity on you constantly.
If the vampire is actually attacking you, this could mean that you are struggling to get away from this person, but it could also mean that you having some kind of health problem; possibly with your blood pressure or heart.
Being pursued by a vampire who is trying to turn you into one of them against your will suggests a strong resistance to change in your life. Be it for better or worse, you are not willing to give up the stability and security of your current situation for a potentially dangerous new path. Vampirism has connotations of immortality, so whatever this change is, you know it's something you can't go back from.
If, on the other hand, you are welcoming the dark side, them perhaps you are ready for an enormous new direction in life no matter what the consequences are.