I've wondered this myself many times and I've only come up with one viable solution. My theory is that the current survivors when exposed to the initial wave of infection were able to create antibodies quick enough to prevent turning into a walker. The fact that everyone alive today remains infected demonstrates that even those whose immune systems were able to handle the disease/virus/parasite (I don't believe we know for certain yet what this is) are only able to keep the infection dormant, not drive it out completely.
Without any resistance from the bodies natural defenses, I.E. death, the infection immediately begins to spread virulently, multiplying exponentially throughout all the bodies core systems. This means a direct bite from a dead or non-immune person would be extremely concentrated, overwhelming the bodies defenses. The lymphs would swell to enormous size, a very high fever would develop, and the victims blood which quickly become toxic, and the organs would begin to shut down. A painful death for certain.
As for accidental ingestion through the mouth - Presumably despite not being shown on the series or in the comics, most people are maintaining basic dental hygiene. (Much of the day to day detail is not shown and is only implied, and in a world without doctors and dentists, health maintenance is EXTREMELY IMPORTANT) If that is the case, and you don't have dirty gums or lesions in your mouth, its actually pretty safe. It is quite likely the mystery pathogen would be destroyed through the natural initial processes of digestion (naturally occurring disinfectant properties of saliva and the much stronger acidity of the stomach) This might also hold true of the nose and ears. (Your body does a pretty good job of filtering out particulate matter from the air and shunting it down the throat.
This pretty much just leaves the eyes and any open wounds. Keep in mind, that since by and large zombies are EXTREMELY dehydrated, their blood will be very thick and congealed, almost like a thick tomato paste. With a blunt force impact, any blood spray will be directed away from the attacker. Same with a slicing type attack like a sword or machete. The only real danger would come from drawing back a puncture weapon, think knife in the eye, and even then, it'd just be a little short range squirt, and I think people would instinctively shut their eyes while they did it. As for an open wound... well if you get contact with zombie blood on your open wound, I think you're pretty screwed. At that point I think you're praying that your bandage has held a seal...
Sorry for the looong post, but thats the only theory I have that I haven't been able to poke holes in.