A vampire is a mythological humanoid that lives off of the blood of other species. The definition and stereotype has changed and varied in different countries, though the modern example tends to be a pale white person with immortality, a dependancy on blood and fangs to suck it out.
Whilst beings vampiric in nature exist (the blood elves' mana addiction as one example), traditional vampires do not (currently) exist in Warcraft. Roleplaying one, especially in the sunlight, will make you look like a noob. If you so happen to be playing one, avoid biting other people and spreading the condition. You'll either permenantly change a person's character against their will, or newbies may think its alright and spread it around Goldshire in a crazy epidemic.
Some people may assume that beings said to be 'vampiric in nature' wandering around are vampires, that vampiric mistbats are literal vampire bats or that having vampiric touch in your shadow priest's talent tree means that vampires do exist in Warcraft. They do not. 'Vampiric in nature' merely refers to something or someone that drains others or things for substenance somehow. Blood elves and the Nathrezim are vampiric in nature, but are not vampires. The bats in the Ghostlands merely drain the energy from certain attacks. The ones in Tirisfal are just meant to look cool, or so happen to be bloodsuckers like normal 'vampire' bats. Being bitten by a bat won't make you a vampire anymore than being pecked by a chicken would.
No traditional vampires have had any mention in Blizzard's lore, thus proving vampires do not exist in Warcraft. There is a vampire-like faction of elves in Wrath of the Lich King called the Darkfallen however, who seem to feast on souls.