In 4E D&D, some zombie creatures-- but not all-- have a trait called "zombie weakness", in which a critical hit kills them instantly. Curious about this, I asked my friend J.D.-- a 3E and 3.5 devotee-- if those previous editions of the game had this feature. The answer was a resounding "no"-- apparently, the undead are immune to critical hits in those editions of the game.
But here's the thing; I like this rule. I get the idea of powerful, unholy undead have an unnatural resistance to a natural 20-- vampires, lichs, wights, etc. But a horde of zombies is a horde of zombies: ravenous, unthinking, slithering, fragile. The sense of terror is derived by their sheer numbers and unendingness-- which is kind of funny in a culture that's, of late, suffering zombie fatigue due to the sheer number of unending cash-ins. Anyway: for me, a critical hit killing a zombie outright makes sense. It also adds to the fun, as my players will be crossing their fingers extra hard in hopes of rolling that nat-20.
Cooler than zombies for me, though, are skeletons-- especially skeletons armed with swords and shields, ala Harryhausen. They're cooler visually, they're not quite as played out while still being familiar, and the weapons give combat encounters more complexity-- there aren't zombie archers or zombie soldiers with zombie polearms. At the same time, I really like the paradox of these fearsome undead badasses also being inherently fragile-- they're just bone, after all, and bones are prone to break and shatter. Which brings me to my house rule: animated skeletons have zombie weakness. A critical hit will kill them instantly, causing their bones to fall into a heap.
The flip-side of this rule is that "thinking" undead-- lichs, vampires, wights, et cetera-- will have an unnatural, unholy resistance to critical hits. Rolling a twenty, even if you don't hit the creature's AC, will still score an automatic hit, but the player will still have to roll damage and does not score any extra, high-crit damage.