Classic zombies are most often very durable and impervious to pain. Even if bisected or quartered, zombies can continue to bite and infect. In extreme cases, beheaded zombies can continue to bite at air in desperation.
Nearly all zombie survivalists are in agreement that the destruction of the brain is the only sure way to deactivate the zombie. Most firearms are at least capable of destroying the skull and brain matter inside. Melee weapons can be effective but are not universally so. Many blunt weapons that are capable of killing a human are less effective at killing a zombie. This is because a living human brain is more delicate, and susceptible to concussions, hemorrages, and neural disruption. Likewise, unconsciousness induced by trauma is a way of the brain protecting itself from further damage. None of these conditions (save for severe hemorraging due to structual damage of the brain) are possible with a zombie.
In order to destroy the brain, one would have to fracture the skull severly and continue bashing until the desired section of brain is destroyed. If lucky, the initial strike can cause a section of the skull to concave and penetrate the brain and cause massive damage, but luck should never be counted on in a zombie apocalypse.
Zombies bodies are typically seen as a bad target. Though they may be as vulnerable to damage as a living human, the after effects of bodily harm are non existent. Zombies do not need their major organ systems. Lungs, stomachs and kidneys are not needed and their destruction or damage will have no effect. Major destruction of limbs will slow zombies even further, but then the threat of crawlers comes up.
Durability to Terrain
Zombies are generally of substandard co-ordination and bad vision, particularly in the dark. As they move across the landscape, many will fall into bodies of water, over cliffs, or fall down scree, resulting in major body damage and possibly crushing.
Durability to Wear
Typically, zombies do not show regenerative abilities, whereas humans are constantly repairing damaged body parts. These include the damage suffered from stubbing toes, walking into obstacles, tripping and so on.
Max Brooks style zombies are in the same class as classic zombies. They are impervious to pain, thought or organ failure. Once the Solanum virus has been introduced to a host, the virus uses the prefrontal cortex as a breeding ground. Despite this, major damage of any of the brains four lobes (in particular the frontal and occipital) will terminate the zombie.
Because of the unique, and as of yet to be scientifically explained cellular properties of Solanum infected tissue, these kinds of Zombies are extremely resistant to overheating, lack of moisture, decomposition, hydrostatic shock, explosives, and the pressure of the deepest ocean depths.
Romero zombies are also in the same class as classic zombies. As such, they share the immunity to pain and have no need for organs or outside energy. It is revealed in Day of the Dead that the section of the brain that controls these zombies is burried deep in the brain, around the brain stem. Because of this, these zombies should be the most resistant to blunt weapons. The amount of force needed to severly fracture the skull and then transfer enough energy though the spongey brain matter is far more than a Brooks zombie. Though this section of the brain may present a smaller target, a single shot should still be able to deactivate a zombie. Hollow point rounds fracture and pop inside and so would liquify most of the brain and even normal shot would send enough force to rupture parts of the brain not directly affected, though this cant always be counted on. Romero zombies also seem to be more resistant to weather, since they can exist for large amounts of time in the elements. Though they aren't shown how they react to extreme weather conditions.