Dhampir
A Dhampir is a being in Roma folklore that is half-vampire and half-human, born from a vampire father and a human mother. They are sometimes said to be able to kill vampires.
The legends
Dhampirs are conflicted creatures, as they cannot turn from either of their bloodlines. They are outcasts among both humans and vampires, for they are neither. They also tend to have many health problems including bi-polar disorder, major depression, insanity, heat syndrome, photodermatosis, and anemia. During their teen years, many dhampirs also have urges of suicide, which can extend into their adulthood if they survive.
Only in extremely rare cases will a dhampir be born and grow to adulthood: generally the female does not come to full term and the baby is lost; in other instances, the mother comes to term and gives birth to a stillborn.
In some legends, a dhampir isn't the direct offspring of a male undead and female mortal, but the seventh male descendant of any line of mortals with a male ancestor who became cursed with vampirism (this later legend depends upon the concept of vampires as blood-drinking high revenants).
Other legends claim that a dhampir could only be conceived by a male vampyr in the first night it rises as an undead, and again this is based on later legends rather than the original vampyr as a spirit creature.
The harsh reality
In reality, dhampirs were charlatans traveling the regions around the Carpathian mountains and elsewhere in eastern Europe. Operating by the original myth of vampyr (old spelling, both singular and plural) as spirit creatures, they were the only ones who could see the spirit and would put on elaborate shows for villages, often wrestling with an invisible foe until it was then trapped in a brass vessel. Usually a dhampir would wait until there was a death in a village. As superstitious as people were out in the wilderness, grief and the environ led to unnatural happenings in the villagers minds... such as seeing the dead walking the village at night. (NOTE: vampyr would take over the recently dead corpse, for as long as it would last, to invade villages. They fed off life force directly, not by blood, sometimes killing victims in close proximity so life leaving the body could be consumed more quickly.) Once fear, grief and superstition took hold in a village following a recent death, the dhampir would "come to the rescue".
Dhampirs in literature, film and other media
Japanese author Hideyuki Kikuchi has written over fourteen novels in his Vampire Hunter D series about a dhampir called 'D', who travels across a war-torn land fighting against "The Nobility" ( who are actually vampires). There have been two anime adaptions of his books, and the anime Hellsing is said to have borrowed ideas from Kikuchi's novels by the way of the dhampir Alucard, who has a very similar parentage to that of Kikuchi's D.
From the Castlevania series of video games, Adrian Farenheights Tepes (also known as simply as Alucard) is the offspring of an unnatural bond between Dracula and a human woman named Lisa. As he grew up, Alucard discovered his strong powers and decided to go against his father and stop his evil doings.
Another dhampir is Blade, from the eponymous comic book series. He became a popular character through the Blade movie made in 1998 and its sequels, starring Wesley Snipes as the main hybrid hero. However, instead of being the offspring of a vampire and human, Blade's mother was bitten by a vampire while she was pregnant with her baby, Eric. As the bite changed Eric's mother, it changed him as well. Eric's mother gave birth, then died; rising later that night as a vampire and leaving Eric alone in the world to grow up half starved and meet the vampire hunter Abraham Whistler (Kris Kristofferson).
Rayne, the main character of the BloodRayne video game franchise, is another dhampir.
Donovan Baine, a character in the video game series "Darkstalkers", is also a dhampir.
Barb Hendee and her husband J.C. Hendee are as of 2005 writing a series of books, informally referred to as the Saga of the Noble Dead, about a dhampir named "Magiere": at the start of the series she is unaware of her heritage and earns a living pretending to be a vampire-hunter.