After death a great deal of blood generally collects in the lungs of a corpse. As the initial stages of the decomposition of the body proceed, internal gasses start to build up. Eventually, about four days after demise, there is a 'bloody purge' from the lungs of the corpse due to this build-up of pressure, and a double lungful of blood is expelled through the mouth and nose. After this occurs, the mouth and nose of the corpse will be full of blood, the face will probably be covered in it, and a large puddle of it will collect around the body.
It has been suggested that this is the origin of the belief that some corpses were not in fact 'properly dead', but had somehow continued to live and had begun to drink blood. Ancient methods of dealing with the 'undead' probably lent even more credence to the belief that they were still alive: the bodies of suspected vampires would be exhumed, and a wooden stake driven through the chest, at which point any pooled blood would spurt out forcibly due to the build-up of pressure, and the escaping gasses would generate a sound very similar to a sigh. This was taken to be the release of deceased's spirit from the curse of vampirism.
Update: 2/7/2003
This writeup originally included the URL of a photo of the 'bloody purge' phenomenon described here. Randofu since has kindly pointed out that the photo has gone, and so far I have been unable to find another. If I do, I'll post the URL here. If you come across a replacement yourself during your travels (well hell, you never know) please /msg me with the URL and I'll add it.