Actually depending on your definition of a zombie, they do exist!
If a zombie is someone whom is pronounced clinically dead, only to "rise from the grave" then that HAS happened. It has been documented in some Voodoo cases, although, they are not like the movie zombies where they crave brains etc.
In Haiti, zombification is a punishment for severe crimes. Coupe poudre is the powder used by a bokur to induce zombification. The active ingredient of coupe poudre is tetradotoxin (TTX), produced in the liver and ovaries of some species of puffer fish (e.g. Fugu rubripes). TTX is a neurotoxin 500 times more potent than cyanide. It acts by blocking the sodium ion channels which enable nerve and heart cells to produce electrical impulses. In miniscule doses TTX causes a near-death state in which metabolic functions are depressed, so that breathing and pulse rate are undetectable. Total paralysis follows, although the brain and senses remain intact. The victim is thought to be dead and is buried alive.
A few days after being buried, the 'zombie' is disinterred and given another powder containing atropine and scopolamine. These are toxic and hallucinogenic compounds from the plants Datura metel and Datura stramonium (both known as the 'zombie cucumber'). This powder, when administered, puts the victim into a permanent state of delirium and disorientation in which they experience delusions and hallucinations. He or she can then be made to do menial work for those against which the crime was committed.
http://neurophilosophy.wordpress.com/2006/05/24/voodoo-zombies-the-puffer-fish/
There have been cases in Haiti where people have awoken after taking this and not knowing who they are, where they are from and having total amnesia. So in this sense they are "zombies".