Vampires are supernatural beings who feed on the blood of the living. Vampires are not considered a "race" in the same sense as gargoyles, humans or Oberon's Children, rather they are former mortals cursed (or blessed) with a supernatural affliction. It does not change the individual's species.  One of the most well known vampires of all is Dracula.
According to Princess Katharine, vampires are vulnerable to silver just as the Third Race are vulnerable to iron. Whether this has any basis in fact or is simply medieval superstition remains to be seen. ("Ill Met By Moonlight")
Greg Weisman has confirmed the existence of vampires in the Gargoyles Universe, though as yet none have appeared in the canon. Greg has mentioned (perhaps not entirely seriously) that vampires in the Gargoyles Universe "have soulful eyes". 
Real World Background
Tales of bloodsucking demons, monsters and evil spirits are practically ubiquitous in the folklore of almost every human culture, from the demoness Lilith of ancient Jewish legend to the chupacabra of modern cryptozoology.
The popular conception of vampires, however, is mainly based on the folklore of medieval eastern Europe. According to this folklore, vampires are undead revenants who rise from their graves at night to feed on the blood of the living. These early folkloric vampires were often described as bloated, ruddy and wearing burial shrouds.
In the 19th century the vampire became a popular figure of gothic literature, beginning with John Polidori's The Vampyre in 1819, which introduced the concept of the suave, aristocratic vampire. This trend continued throughout the 19th century, culminating in the publication of Dracula by Bram Stoker in 1897. Stoker's novel is still considered the definitive vampire novel, spawning an entire genre of vampire fiction that includes books, movies, TV shows, comics and even musicals.
- Vampire at Wikipedia, the Free Encyclopedia