In 4th edition, there's a 'race' called revenant, which is basically an option for a Crow-esque semi-undead body holding the soul of a person who was betrayed or who is needed by the goddess of death to fulfill some sort of mission. If, say, your favorite dwarf is killed, you could get resurrected, or you could work out with your DM that you've been brought back as a revenant. Then you pick the 'dwarf revenant' option, so you've got a mix of dwarf powers and undead vengeance powers.
So far, so good. It's cool. It's flavorful.
Early in 4th edition, the digital Dragon magazine published a couple feats that you could take to reflect a 'vampiric heritage.' Y'know, like if you wanted to play someone like Blade, born to a mother who was maybe bitten by a vampire but not turned, or something like that. It gave you the ability to drink blood to regain health. Again, cool, flavorful, gives PCs something fun.
Then in the 'Heroes of Shadow' book, they created a whole race of people who had connections to vampires. I'm not sure exactly how Vryloka work -- if they were people granted semi-vampiric powers by an undead lord, or if they were some sort of vampire race (which, while not consistent with Bram Stoker, is at least an idea that shows up in some vampire low). Okay, whatever. You're part of a proud bloodline with magical powers that make you somewhat immortal. Independently there's nothing wrong with that.
The same book, though, included a straight-up Vampire 'class,' which is necessary because 4e doesn't use templates. You could make, say, an elf vampire, or a halfling vampire, and the vampire class gives you options that fit all the classic Dracula stuff -- turning into a bat, beguiling with a gaze, sucking blood, climbing on walls. Good times. Very classic, and since it's a race you can combine it with any class and, if the DM's cool with it, you can have a full-fledged PC vampire. Sure, it's possible to have something like a warforged vampire (I guess he preys on oil cans), but hey, it's fantasy. You can have a vampire curse on a golem if you want.
But.
You can also make a revenant who in his former life was a vryloka, whose class is vampire, with the vampiric heritage feat. So apparently he was from a semi-undead race, and his mom was a full vampire, and later she turned him into a full vampire too, but then was destroyed and reincarnated into a different type of undead body. Yes, in 4e, you can have a quadruple vampire.