Comparing a dog's mouth with a human's mouth is sort of like comparing apples and oranges—really filthy apples and really filthy oranges. Both species' mouths are hot, damp places teeming with roughly equal populations of bacteria. Neither would be described as clean, and any question of comparative cleanliness is irrelevant because so much of that bacteria is species-specific. Most of the germs in your dog's mouth aren't going to be a problem during a big, wet doggie kiss. You're more likely to run into trouble kissing another human than you are a dog, because bacteria from a person's mouth will feel equally at home in yours.
Of course, not all bacteria are species-specific. Dogs and humans can and do transmit some germs to each other via the mouth, so if your dog is the type that likes to lick faces (is there any other type?), there are a few precautions you can take. One, try to keep your dogs from picking up any external bacteria by keeping them out of the trashcan (and away from rancid food), and away from wild animals (lest they contract rabies). Two, keep them healthy: up-to-date vaccines, good external and internal parasite control, regular teeth brushing, etc.
And then, pucker up!
While we're at it, let's tackle two more things we're often told about canines: 1) Dogs lick their wounds and they heal very fast, and 2) Dogs don't get as many cavities as humans. There are simple explanations for both. Licking the wounds gets rid of dead cells and dirt, just like when we wash our wounds. The immune system takes it from there.
As for cavities, they're largely caused by the bacteria Streptococcus mutans. These bacteria feed on sugar, which is far more common in a human's diet than a dog's. Hence S. mutans prefers to live in our mouths, not Fido's.
[This Big Question originally appeared in 2010.]