We know very little about vampires in Harry Potter, but we know they’re protected from anti-vampire violence by the Ministry of Magic. It’s strongly implied they can control their thirst for blood – they even have blood-flavoured popsicles, presumably to help control the craving.
That said, they’re hated. Vampire-hunting is illegal, but a lot of people are itching to do it.
Most fans believe that there will be a vampire at some point in the series, because they’ve been mentioned so many times. Since we don’t know Rowling’s “vampire rules”, it may be possible that one of the current characters is a vampire (in some traditional vampire stories, they can go out in the sun, for instance).
Snape seems a likely candidate, though given Rowling’s penchant for surprises, it may be someone else. For all we know, she’s scrupulously avoided putting some character out in the sun, and we just never noticed it because it was too subtle.
The only other thing we know about them is that they’re pale and gaunt, and afraid of garlic. We’ve never seen anyone eat garlic in the series, IIRC, and “pale and gaunt” describes half the characters in the story.