There seem to be an infinite amount of them, and in all levels they continually increase in HP as the game goes on, eventually reaching a point where the only feasible way to kill them is with weapons that are automatically one-hit kills. There is no way to win zombie mode, the only goal is to survive as long as possible before eventually dying, although most of the later maps in Black Ops contain complex easter egg missions with unspoken objectives. In the earlier Zombie maps from WaW the zombies weren't as "zombiefied" and still resembled humans, but in the Black Ops maps they become progressively more corpselike and mutilated.