The popular modern zombie is infectious, and being bitten by one will result in gradual deterioration of the victim’s health, followed perhaps days later by death, and then shortly thereafter “turning”. I suppose that the actual death part is irrelevant and that turning may occur prior to death; zombies do not seem to attack other zombies. They hunger for the flesh of the living, and this is sometimes specifically the human brain and nothing else.
Now, to kill a zombie, one must sever the head from the body or destroy the brain. This is commonly mentioned in zombie moves (a quick Google reveals at least Shaun Of The Dead, Severed, Return of the Living Dead: Necropolis, and IIRC all of Romero’s Of The Dead films). This means that the brain must be at least partly intact, enough at least to control the movements of the body. That part of the brain is near the back of the frontal lobe, so one assumes that if that part of the brain is destroyed or devoured, the zombie will be incapacitated and unable to continue functioning.
Zombies eat humans. Humans take time to turn into zombies; they have to die and the corpse must be in sufficiently good condition to become mobile. So how does the epidemic spread? This doesn’t seem to be a question that gets answered to my satisfaction. One-on-one, it’s probable that an unarmed human could escape a zombie, probably being bitten in the process, later dying and turning. Many-to-one, though, it’s probable that the zombies would devour the human to the point where the corpse was incapable of turning. This is exacerbated by any stipulation that zombies must eat brains. I cannot believe that a zombie epidemic could be caused by bite incidents. Another possibility might be that as soon as the human is deceased, the zombies become disinterested in the corpse, leaving it to rise later as one of them. But this conflicts with much of the popular media, which have zombies tearing people apart and walking around with severed limbs, etc.
(I Am Legend spoiler in this paragraph) It might be necessary to devise some other vector for transmission of the infection. In 28 Days Later, this is done by transmission of blood into the system somehow (ingestion, I suppose, or in one case having it come into contact with the unprotected eye); in I Am Legend, endospores are carried by the wind, infecting anything coming into contact with them in a similar manner. In Dead Rising, there seems to be an insectoid vector which also serves as a controller (something which most modern zombies lack despite the literal meaning of the word ‘zombie’).
I still don’t seem to have a good, definitive answer for how this sort of thing spreads. At least it leaves room for artistic license. Additionally, for the purposes of most games, the cranial criterion is forgiven due to the fun factor of blasting away at zombie torsoes in the knowledge that they will eventually drop.