Zombies in popular fiction are sometimes able to survive without a head. Can a zombie in D&D do the same?
This is relevant for an effect like the vorpal sword's, which says:
When you attack a creature that has at least one head with this weapon and roll a 20 on the attack roll, you cut off one of the creature's heads. The creature dies if it can't survive without the lost head.
Best Answer
A standard zombie would be killed
There is nothing in the zombie description to indicate that it can survive without a head. So by default, decapitation by vorpal would kill it.
Some further support for this is given by the Undead Fortitude trait that says that a zombie has a chance of surviving normally fatal damage unless the damage is radiant or a critical hit (and a natural 20 from a vorpal sword would also be a critical).
This is likely meant to represent the classic film zombie that is incredibly hard to put down unless it takes massive damage and/or you blow its brains out!
Of course, as a DM, you are totally free to adjust this and come up with a zombie that's even harder to kill (though it must either have some other vulnerability or else possibly a higher CR to compensate).