Downplayed: A Technically Living Zombie that can feel no pain can shrug off most injuries that would stop a normal person, like broken bones. They can still be killed by bleeding, stopped by nerve damage, debilitated and even killed by gangrene... But the fastest and most reliable method is to break it's spines, neck, or destroying the brain.
the nervous system is the only system working, destroying that stops the zombie stone cold.
Parodied: Zombie heads are like soufflés; the slightest disturbance causes them to collapse into goo.
Zig Zagged: There are two variants in universe that follow different rules. Biological whether technically living or parasite animated don't stop unless they're headshotted. However aiming exclusively for headshots is Awesome, but Impractical. Force can still slow them down however. The Boring, but Practical way to deal with them is to shoot them enough to disable and then shoot them in the head before they get up again. Supernatural zombies aren't stopped by being shot in the head - every last piece of it demonstrates Organ Autonomy. Fire however will cause them to burn up in seconds.
Averted: Zombies can be killed like a living person, it just doesn't hurt as bad if you shoot them in the guts.
Enforced: "Look, it's a zombie movie. If they can be killed by normal means, it's just not a zombie movie."
Lampshaded: "All we know about them for sure is they smell really, really bad. Always go for a headshot, just in case."
"You think cutting off my pretties' heads will stop them? Bwahaha, my potent magicks would sustain them even as a shambling bag of flesh and bone!"
"We have identified a new type of Creature, which has all but completely replaced the standard 'zombie'. They have evolved a thick, bulletproof carapace covering everything from the crown of the head, to the shoulders and collarbones (except for the lower mandible), which is filled with cerebrospinal fluid, like a second skull. It has been proven to deflect everything from buckshot to minigun rounds. Headshots and decapitation are now useless tactics."
"It is a bad idea to shoot Xenoparasite hosts in the skull. The parasite will simply be extruded, and will most likely harm you-perhaps fatally!-while you're getting over the initial shock. Removing the limbs, which may themselves be infested, is also inadvisable. Meet the FTX-35 Thermal Lance, your new best friend..."
Discussed: "If horror movies have taught me anything, it's you have to shoot a zombie in the head to kill it."
Deconstructed: "Center of mass" is taught so widely for a reason. One headshot's a fluke - thousands consistantly is impossible. The fact that it's a zombie's only weakness thus makes them very difficult targets, esecially at long range.