UPDATE: Everyone's infected! Problem solved. (18 March 2012)
Let's get it out first that this will be dealing only with the television series, not the comic book. The comic book nicely avoids this problem all together by having everyone who dies for any reason except brain injury reanimate.
Aside from the first half of season two being about two episodes stretched out to seven and not getting anywhere for no apparent reason (money?), and the improbable aiming skills the characters have (try making a head-shot every single time while both you and your target are moving top speed - bet you can't!)*, and the glaring inconsistencies with how the zombies work**, the whole business of zombification would render the story completely impossible from the start.
In the TV series "The Walking Dead" the only way someone becomes a zombie is to be bitten by a zombie, escape, die, and then reanimate. It doesn't help to be bitten and then devoured because there's nothing left to reanimate. You have to kill the zombie (kill, they're already dead!) or run away, and then go croak somewhere because a zombie bite is always fatal. Then when you die you have to be far enough away from the zombies to not have your body eaten, because reanimation isn't instantaneous. Dr. Jenner stated that it takes a few minutes to a few hours before the brainstem starts up again, so if you're eaten within that window you won't zombify.
Anyone who dies but is not bitten will not zombify, as the mess of bodies in the traffic pile up attest to. This leads one to wonder if the process of zombification takes so long and requires a bite from a creature that certainly won't say "he's dead, I'll attack a living now and leave his body to zombify," you're going to have a hard time reaching plague proportions. Consider next the fighting abilities of humans and zombies. Zombie to human kills are at least eight to one. Anyone with a gun will kill as many zombies as they have bullets, guaranteed. Unless a minimum of eight zombies attacks any person, no matter how big or strong or fast or smart or well armed, that person will survive. When we combine these two problems there is absolutely no way we can have a global zombie pandemic with only a handful of humans left. The mathematics just doesn't work. If zombies are so damn difficult to make and so damn easy to kill there is absolutely no way to get a zombie apocalypse going. Maybe a couple towns will be caught off guard, but not an entire country, and certainly not the whole planet.
Don't say that maybe one zombie bit ten or twenty people before being put down. They don't do that. A zombie will keep attacking someone until they eat the person or are destroyed. They are not smart enough to sacrifice themselves by biting several people to spread the plague before being killed. Zombiism doesn't spread fast enough for a zombie to bite someone, have them turn, and then move on to someone new. Unless we eliminate one or both of the above facts - the dificulty of zombification or the kill disparity - there is no way "The Walking Dead" can happen. That's what you get when you try to have dead zombies who spread like living zombies.
*Andrea is the only one that has ever missed, and only because missing was relevant to advance the story, and she still very nearly killed Daryl (with a head shot, as if I needed to mention it) at 200+ yards, from an unsupported prone position, facing the sun, with an unknown number of head winds, with five friendlies just feet away from Daryl, on the second time she's ever fired a gun. Damn! Now that's beginner's luck! Her stupidity could easily have killed one or more of six people. Even if there was a zombie there's no way a thinking person would have attempted a shot like that.
**Sometimes they hunt by smell, other times they don't; sometimes loud sounds like gunfire will attract them, other times you can teach people how to shoot all afternoon and attract no attention at all; whatever reanimates them only restartes the brainstem but people can hit them anywhere in the head and still bring them down, going so far as to have Daryl shoot one with his crossbow up through the jaw and hard palate into the nasal cavity and kill it after it started gnawing on his boot even though the bolt would have only gone through the frontal lobes, which were explicitly stated to not restart with zombification.