The instinctive licking of a wound is deeply programmed into our brain and probably dates back to our oldest ancestors. Many animals have also this "weird" response to lick an injury, like dogs, cats, rodents and primates.
Researchers at the University of Florida at Gainesville have discovered a protein called nerve growth factor (NGF) in the saliva of mice. This protein can heal a wound twice as fast as an untreated one, which explains why mice lick their wounds.
Humans on the other hand do not have this protein (or probably lost it through time). Nevertheless, researchers discovered antibacterial agents as secretory IgA, lactoferrin, lysozyme and peroxidase. Although it has not been shown that licking a wound will disinfect it, it certainly helps to remove larger contaminants such as dirt.