The issue of whether or not zombies eat the brains of their victims is a long-standing variable in comprehending the creature's mechanics. The theories out there are manifold, but in the end, only one must be correct. Contribute your own theory to this page, and please try to come up with some scientific explanation for it. Understanding this could be the key to knowing how the Z brain works and/or the development of a cure.

Necrowerx
It depends on whether or not you follow the theories laid out in Max Brooks' Zombie Survival Guide, for one. I have trouble with a number of them, though I like his book overall, and I favor the major part of the Solanum virus theory.
Consider this: if the "goal" of a zombie is simply to reproduce/replicate, then biting a human host anywhere on his body is sufficient for successful infection and thus reproduction. The urge to bite may be as strongly instinctive to the zombie as sex is to the living (there's a disturbing, gross thought in there somewhere) Now, according to Brooks, zombies don't eat for nourishment, as the digestive and cardiac systems are totally shut down anyway. So to simply propagate the virus, a simple bite would suffice. Here, however, he runs into an apparent self contradiction: if the zombies are not eating for nutrients and cannot digest food anyway, why would they engorge themselves by consuming their victims totally, when given the opportunity? That doesn't leave any possibility of reproducing another zombie, and so is antithetical to the virus's continued existence. Even more so, if zombies don't need to "eat" (per se), why would they favor any particular organ, such as the brain? Again, this is even more self-defeating than eating regular internal organs or flesh, because the brain is absolutely integral to the existence of the zombie itself - no brain, no zombie.
Personally I've always viewed brain eating zombies as a bit of whimsical Hollywood fun. "I can smell your brain!" declares a zombie in one recent flick.. I don't believe zombies possess the ability of speech, either, so, in my opinion, no, zombies don't go after your brain specifically - that's simply a Hollywood notion.

I (TonyPro) have resigned myself to devote most of my efforts in the near future to contemplating this and developing a solid theoretical base.

TonyPro: For a virus or bacterium to spread throughout the body as fast as the zombie infection would, it would require hugely over-stimulated peripheral neurons (the nerves that run most functions in the brain) in order to keep the brain alive. In this case, the Z infection would need huge doses of myelin (a substance that sustains these nerves) in order to keep the zombie's brain alive; more than could be produced by the zombie's brain alone. In a nutshell, without large quantities of myelin, the infected person's brain would go haywire and they would go into a seizure, forget to breathe, and die. Myelin is produced in the 'grey matter' region of the brain; so in order to survive, a zombie would have to munch on the occasional cerebellum (myelin is easily absorbed into the bloodstream where it could reach the brain).
Note: I have since had many qualms about the above theory, and no longer believe it to be wholly possible, as myalin generally attatches itself to a cell and is noncommutative. I will update this moar.

Dragoon1218: i think this is simple zombies would not be able to get to the brain the skull is such a hard bone to break to bite threw it would not happen for days and most likely break all of their teeth before it could ever reach the brain and last time i checked nawing with your gums was not an effective way to get threw anything other then soup or pudding and possibly jello. but lets say for sake that they do eat brains this would allow the zombies to not spread as in if the is no brain nothing in the body will function if the body lacks function then no movement which means no zombies

StrykerPez: I think the misconception of zombies eating brains comes straight from the movies. I think that the only reason zombies would even consider to eat people is for sustainance. And then they would go for the easy tasty parts. Other than that, attacking humans is strictly due to their primal instincts and nature.

Renegade13: I also think that the eating the brain thing is totaly fictional because1) they probably couldn't get to the brain and 2) they couldn't turn other people if the brain is gone.

Happyman: You guys gotta rememeber that people only use up to 20% of their actual strength, so if the zombies could harness the other 80% they could bite into a skull, or... Even worse... EVOLVE AND USE TOOLS. That'd just be bad news in general. And who says the Brain isn't Tasty!

Dragoon1218: even if they could muster that strenght again still the teeth would break on the skull and that would stop them from getting in any more and from biting anyone else ever so for our sake lets hope they all try that and no one gets infected then we have like 20 harmless zombies that we can use for the enjoyment of the people by making them look stupid in silly outfits such as zombie clown zombie redneck zombie drag queen zombie with no eye and random funny object sticking out of zombies eye socket also this would allow us to do futher research of certain things and the effects it has on the zombie long term studies of this could yield a permant solution to this proplem