Many animals (including humans) will "lick their wounds".
It is noted that "wounds" in the mouth are some of the quickest healing, and in some cases, bare muscle in the mouth can generate mucosa and heal over.
I find that sometimes I can remove slivers with my teeth, and a small sliver can certainly inhibit healing.
Anyway, there is some evidence that saliva has some disinfectant nature, and some animal studies indicate that it can actually speed healing.http://en.wikipedia.org/wiki/Saliva#Disinfectantshttp://en.wikipedia.org/wiki/Wound_licking
There are pet-borne diseases. Most dogs in the USA are vaccinated for rabies. However, cats, for example, can carry "Cat Scratch Fever". https://health.google.com/health/ref/Cat+scratch+disease
Pasturella also seems to come up frequently in discussions.http://en.wikipedia.org/wiki/Pasteurella
You will have your own "Flora" including skin bacteria, mouth bacteria, and gut bacteria (as well as yeasts and other eukaryotes). Your body will have a complex system of keeping the bacteria and yeast where it is supposed to be including inhibitory proteins and antibodies in your saliva. Small amounts of bacteria can enter the body with things like dental work, and is generally not harmful. However, in general getting bacteria inside of your body is bad.
Your dog will also be colonized with its own set of bacteria and yeast flora including moth flora.
Assuming it is your own dog, you will likely have had some contact with your dog's flora and may have some immunity to whatever it has. However, that may not be true of someone else's dog.
There have been reports of severe infections resulting from pets licking wounds. See the Wikipedia article above.
If you have a small wound, there is no problem with licking it yourself (except in the presence of toxins).
It probably won't hurt if your own pet licks it. But, it does carry some additional risk.
It would not be advisable to allow a pet that you haven't had close contact with lick it.
Clean water, soap, and an antibacterial dressing is always a good idea.
If you have a large wound, licking it is probably not advisable due to increased infection risk. Soap, clean water, and antibacterial dressing is still good. Seek medical attention if you have any doubts, you think it may require stitches, or if it is in a place that could cause disability or cosmetic problems.
Monitor for signs of infection or movement of infection out of the immediate wound area.
There are also conditions that could put you at higher risk from bacteremia, including heart murmurs and cardiac valve problems, as well as internal prosthetic devices, in which case sterile procedures would be advisable.