When you die, your skin shrinks. This can cause the illusion of your fingernails still growing and your teeth getting longer. It was this that caused people to believe that certain bodies belonged to vampires, and as such were burned, staked through, etc. during the (Middle? Or Dark?) Ages.
Certain settlements also believed that animals would not dare walk over the graves of vampires and other supernatural "humans", so they would take animals such as horses or dogs and walk back and forth in a cemetery. If the animal would not cross over a grave, that grave was promptly dug up and the body was burned, staked through, etc.
Grave robbers didn't help this, either. Since science wasn't exactly near what it was today, particularly medical science, various medical institutions would hire certain individuals to, ahem,
acquire cadavers for them to cut open and study. Any grave was fair game, but the results were that the more superstitious folks would equate a missing body + freshly dug dirt to be the work of a supernatural entity, rather than that of their fellow man.
Thus, they'd take measures to ensure the vampire would return (I.e. burning, staking through, etc. the coffin...
)