Child of the Storm has Remus Lupin use the Pratchett quote 'as many kinds of vampire as there are kinds of disease', with the corollary that some are fairly harmless. Some, however, are major players, with the four Courts from The Dresden Files mentioned, with an additional fifth Court to include classic Dracula vampires:
White Court: The Western Anthrophage. Each House within the Court is a different breed of Emotion Eater. They are, technically speaking, mortal and the most human of all vampires, reproducing sexually (with the resultant offspring being human until mid puberty and they make their first kill). Because of this, they are near impossible to tell apart from humans at a glance. They are also all ridiculously good looking and owing to their relative lack of physical power and favouring of Psychic Powers, prone to manipulation and Chronic Backstabbing Disorder. They were behind the writing of Dracula (to undermine the Grey and Black Courts) and, as Harry Dresden suspects, Twilight, which has apparently caused vampire attacks to quadruple since it was published. Thomas Raith also appears in a side story, Chaos Reigns.
Red Court: The Mayan Blood Demon. Hairless anthropomorphic bat monsters in a human disguise based in Central and South America, they have the traditional weaknesses but can be killed by good old fashioned violence (lots of it.) Their saliva is also a powerful narcotic. They are generally disgusting. They turn humans halfway, resulting in a Dhampyr until they lose control and make their first kill. Among the most organised, innovative, and overtly political powerful, having a strong hold over much of Central and South America, they are led by the Red King, who is around 10,000 years old. Also known to occasionally feed on cows, sparking the legend of the Chupacabra.
Jade Court: Reclusive Asian Vampires. They don't get involved with the affairs of others all that much.
The Grey Court: Classic Dracula vampires, originating with Varnae, the first vampire, created by a spell from the Darkhold in the last days of Atlantis, 17,000 years ago, who went on to sire a large Court, and was a major power-house, being on record as having fought Thor, Odin, Vili, Ve and Bor at varying points in history. he was last seen during the Black Plague. Since then, Dracula has taken over as King of the Grey Court. The three day rule applies on turning, with the person turned having, in the meantime, the powers of the vampire but their own mind. One or two part-vampires of this kind exist, Blade and Spitfire II (the latter as a result of a blood transfusion from Blade). They are hinted to be a particular target of Asgardian purges and themselves attempted to wipe out the Clan Akkaba, heirs of Apocalypse. The Clan responded by summoning the Phoenix and attempting to bind Her to their will in Vienna in 1897. Since the Phoenix was none too fond either of vampires or of being controlled, it ended very badly for both the Clan and the Court, with the two being almost entirely wiped out. Only Dracula and the girl nominated as host survived, the former because he got out in time and the latter because Albus Dumbledore pleaded for her life.
The Black Court: an offshoot of the Grey Court, the result of a curious necromancer trying to turn a corpse into a Grey Court vampire rather than a living being around 8,000 years ago. The result was essentially a living cadaver that steadily decays and withers, one to which the three day rule did not apply. They are essentially experiments gone wrong and they hate to be reminded of it (while just about every other group naturally does so at every opportunity, and nowadays, within easy earshot). They also suffered greatly from the publishing of Dracula, since unlike the Grey Court, they're not very good at passing for human.
Others are hinted at, such as SeleneGallio, with even Voldemort dabbling in it a little bit, and a mysterious figure known only as 'The Welshman', a vampire from outside the Court system powerful enough to scare off all the others and largely responsible for keeping other vampires out of Britain. He is, apparently, a Friendly Neighbourhood Vampire. Though, as Word of God notes, this is for a given value of friendly - he will keep other vampires out of Britain, he will even keep crime down in his chosen city of Cardiff... but he's not exactly going to be putting on his cape and becoming Super-Vamp, defender of all that is good and true, any time soon.
Ebony Dark'ness Dementia Raven Way of My Immortal is a vampire, but it doesn't seem to affect her much except for being Immune to Bullets, being pale, drinking blood, and having a liking for Count Chocula cereal. She does dislike the word "cross" to the extent that on one occasion she types it "c-r-o-s-s" and on other occasions changes it to "pentagram", as in "She looked like a pentagram of Lindsey Lohan and Hillary Duff", but on one occasion she still wears cross-shaped earrings. Apparently she could be killed with a "steak." (She had better not go to any barbeques.) Harry "Vampire" Potter might or might not also be a vampire.
Thirty Hs features "astral vampires", which dwell in space and are able to bite even when only their heads remain. Harry Potter punches their heads off and throws them back in time to the planet Mars, where they bite cavemen, and so now there are vampire cavemen on Mars.
A Growing Affection has a blood-drinker demon clan, that drinks Human blood to increase their powers and enslave the people they feed on. Doraku (the only representative of his clan seen) dislikes being called a vampire but admits his clan is the source of the vampire myths.
Fluttershy in Nosflutteratu doesn't burst into flames when exposed to sunlight. It does weaken her though. Her vampiric nature is also the in universe explanation for The Stare. The idea that vampires don't have reflections or cast shadows is just a myth though.
C.C explains in More Than Just a Man that most vampiric weaknesses are either something completely logical or quirks of particular vampires: Garlic simply smells bad to their enhanced noses, sunlight is irritating as they can no longer tan, crosses were simply Dracula's thing, and being forced to count things is on account of some vampires developing Obsessive Compulsive Disorder as a coping mechanism. Lastly stakes through the heart kill most vampires because they get Stronger with Age and it takes a few centuries for them to heal fast enough to survive being stabbed in the heart. Though even she doesn't understand why salt water weakens vampires. Furthermore, most of the more fantastical powers aren't real. For example, shapeshifting is really vampiric hypnotism to make someone think a vampire transformed. Lastly, it takes roughly a year for someone to fully change into a vampire, longer if they don't consume the massive amounts of nutrients the change requires. Also, the enhanced physical abilities (at least to begin with) is based on what the victim was capable of beforehand: an Olympic athlete would become superhuman but someone like Lelouch would only be on par with a trained athlete.
This trope is played straight in A Magus at Mahora when Shirou says "Our vampires are different" and goes on to describe what vampires are like in his home world, the Dean and Takamichi are horrified at the comparison to their worlds vampires which are a lot more 'human' in nature; Takamichi's comment sums up their thoughts fairly well:
Atlantiana Rebeckah Loren from the mildly famous Twilight fanfic Forbiden Fruit: The Tempation of Edward Cullen is a dhampyr - half vampire, half (human?) witch. Her "vampire powers" are awakened by having sex with Edward Cullen, but so are her witch powers, which include being able to make trees light on fire and take copious amounts of drugs and still be able to drive safely. However, it's not made clear what the difference between the her witch powers and vampire powers are, and the story abruptly ends before we can see the extent of them.
Vasile, the Arc Villain of Sleeping Beetle, is identified in-story as a strigoi mort, which is effectively a vampire ghost. He's bound by some of the usual vampire rules, but also by certain ghost rules, and his powers are a little different; for example, he changes into an owl instead of a bat.