Does he crave brains?
Well painstakingly creating a monster that people mistakenly call by your own name can create a powerful hunger, though for brains I’m not sure.
By this pool is reminding you, in his/her own winsome way, that Frankenstein is the name of the Mad Doctor, & not that of his creation.
And, in Mary Shelly’s novel, the Creature can speak, and reason! Even read! He is swift, agile, deft & cunning. All unlike the film version, & quite un-zombie-like.
Depends on the version of the monster (hereafter referred to as “Frankenstein”)—by some accounts, he’s literally an animated corpse, kept “alive” by an artificial charge of energy (sometimes to the point that, if he’s injured or something, electrical arcs will fly out of his wounds!). This could be considered something like a battery-powered zombie, I suppose.
On the other hand, a number of other sources depict him as basically just being a “normal” person, who just happens to be made out of the parts of dead people. No more a zombie than, say, someone who’s had all of their internal organs replaced by transplantation. “Unnatural,” maybe, but not undead.
Of course not, the monster he created doesn’t crave brains. He craves acceptance and love! 
Brendon
I think this is a very good question. I must make some comparative notes and I’ll be back with my conclusion… and charts!
And hopefully pie.
Is Jesus a zombie? he was reanimated from the dead, although he craves souls.
mm
I’d say not. Zombies generally have to invoke some kind of outside power, like magic, or an unknown transforming plague to explain how they can remain dead yet act alive-ish. They generally don’t think, or feel pain, and can spread their zombiehood. Frankie’s monster i’d say is technically alive, in that he does think, feel pain, and probably could knock someone up (no wonder the Bride’s looking peeved). And he can’t spread his monsterhood through bites or killing. I’d say even if he was a type of zombie, he’s different enough that a couple of different classes of zombie would have to be used.
Frankenstein is a Golem. The old Jewish story of a man created from clay.
This is the standard mythological root at least.
Jim
Frankenstein’s Monster was an homunculus, created from base matter via principles derived from a combination of Enlightenment-era natural philosophy and Paracelsan alchemy. Traditionally, homunculi were made no larger than a foot in height. Victor believed that working on a larger scale would make the work go faster, which indicates that he kind of missed the point about why they were built so small in the first place: because the small ones are much easier to stomp on when they turn on you.
Zombies, of course, only exhibit a specific craving for brains if reanimated by 2,4,5-trioxin.
So Jesus is Stormbringer reincarnated then?
In D&D, F’s Monster would be a form of advanced flesh golem.
In the book, the monster was intelligent and articulate; it also, IIRC, had a highly efficient digestive system, so it could subsist on a scrappy sort of vegetarian diet (nuts, berries, tree bark, that sort of rubbish.)
Since Frankenstein’s scientific insights were at least partly derived from his study of mediaeval alchemical texts, Terrifel’s suggestion that the monster is a sort of a homunculus is probably closest to the mark.
Make that a flesh golem that has been subject to the Awaken Construct spell (the current version of which can be found the in the Spell Compendium).
I say he’s a zombie in the sense of being constructed entirely out of reanimated flesh, IF that’s how you define a zombie.
If I’m not mistaken, “real” zombies were people who were drugged and thought to be dead, so they could be taken from the grave as slaves by other people and no one would know that they were still alive somewhere. The drugs left them in a state where they had no will of their own. So, part of the definition of a zombie may just be the lack of free will.
I would say a zombie, in the pop culture definition, would be an entity comprised mostly of reanimated flesh with the absence of free will.
The movie zombies crave flesh, but much of that is up to the individual interpretation of the word as it applies to that particular work of fiction.
Then comes the question of what makes something a “monster.” Is Frankenstein’s creature, in fact, a monster?