To be blunt, any nocturnal carnivorous or parasitic supernatural being will be labeled a "Vampire" by folklorists. Entire books have been written on the subject.
Romanian mythology has what's called strigoi. Quick notes:
Unlike Russia's upir, which is a walking, bloodsucking corpse from day one, strigoi start as harmless poltergeists.
Some ill-omens can point to a human rising as a strigoi, but they're just indicators of what's possible: stuff like a black cat walking across the grave, moonlight falling on it, monkshood growing nearby, the list goes on and isn't conclusive.
Driving a stake through the heart of a recently deceased strigoi vio (or human doomed to rise as a strigoi mort) will keep it from rising altogether. If that can't be done, wait until the spirit manifests through poltergeist activity and then call in the priest to exorcise it.
The ghost grows increasingly more volatile until it's spent seven whole years in the town it inhabited in life. Then it's free to wander around the land.
Makes more of 'em by fathering children instead of with an infectious bite. The kids will become strigoi mort after death.
Strigoi are also frequently described as being able to turn into owls, much like modern vampires turn into bats. "Strigoi" in fact is etymologically related to the word "Strix", "owl" or "screecher" in latin.
Romanian lore also includes an Eldritch Abomination variant called a Varcolac, that apparently has the ability to swallow the moon for a small amount of time.
A majority of European vampires (or revenants, see first point) are corpses with a ruddy complexion, skin and nails that have fallen off to reveal new ones below, and have gained weight/bloated up. In short, they look like bodies in the natural process of decay.
But to the average ignorant medieval peasant they would look like they were alive, especially with the nails and hair and bloating.
Malaysian vampire lore includes a truly bizarre creature called a Penanngalan, which looks human by day, but by night detaches its head and flies (trailing its intestines) to people's windows where it uses its long, thin tongue to suck blood. It can be killed by filling its body with glass (so it shreds it's organs on re-entry) or trapped with thorns on a windowsill. Notably, this vampire, unlike most mythological variants, is vulnerable to sunlight, but only in its detached form, which is why trapping it until sun-up is a viable way to kill it.
Filipino mythology has basically the same creature, but instead called a Manananggal, that detaches its entire upper body and grows bat wings.
The Japanese have two very similar creatures, one that detaches its head and is basically the same as a Penanggal, and one that simply stretches its neck out.
And finally, Burma has an all-male variant called a Kephn, that is arguably worse than all of the above because it feeds on people's souls.
In the Andes, there is the Pishtaco. Instead of drinking your blood, he drains the fat out of your body and sells it to the white man on the coast, who uses it to grease his machines. After he's dried you out, he cuts you up. Makes an appearance in Death in the Andes by Mario Vargas Llosa and on the ninth season Supernatural episode, "The Purge".
India has the Vetala, an evil spirit that inhabits a corpse, transforms it into a batlike monster and drinks blood. It's notable for functioning more like a trickster spirit then a vampire, and enjoys rhymes and riddles.
Ghana has the Adze, a disgusting, hunched gnome that takes the shape of a firefly to feed on blood.
In Finnish folklore, a child born out of wedlock, murdered by its mother after birth and buried in forest would stalk after her for the rest of her life, seeking to suck her breasts, not for milk but for blood, until she died. If they couldn't find their mother, they could go after any unfortunate woman. The stories usually depicted them as naked, paper-white toddlers, in spite of the murder taking place when they were newborns.
In Albanian folklore, a 13th century tale speaks of the Dhampyr. A soldier goes to war but he promises his wife to come back to give her a son, legacy and stuff. Of course, he dies, yet still comes back, undead. He has the son and raises him, all this time not going in the sun. When his wife tells his mother that she is living with him she tells her that the dead are dead and the living should not mess with that. They get him high on weed (not making it up) and expose him to the sun. The end. How do we get from this to Blade, Blood+ and Vampire Hunter D? Who knows.
In China, there are the Jiangshi, which are something of a mix between the traditional Slavic vampires and zombies. One notable difference is that the Jiangshi is not free of rigor mortis: Given enough time after its death, the creature will get so stiff that it will be able to move only by hopping.
Asturias (northern Spain) has the Guaxa, a nocturnal creature with the aspect of an extremely old woman with big owl eyes and a single, needle-like tooth that uses to suck the blood of children. It can squeeze in through any crack, and sleeps by day in a cave or a hole in a tree - making it oddly similar to the "Teliko" seen in The X-Files.