Well, if you're going with the spirit of the modern virus-zombie myth (err, the one that makes zombies resilient and inhuman rather than deranged cannibals, at least), most of the fiction implies that part of their toughness is the result of reduced nervous system functionality. That's how they don't feel pain, &c. Based on that trope, most of a zombie's brain would be dead weight, with only the most primitive bits (which, inconveniently enough, tend to be deep inside the head) being necessary for the body to continue functioning.
That means the kind of blow that would easily kill a real person isn't really enough -- blood loss isn't going to stop a zombie (somehow), concussions don't affect them, and you can really go to town on their frontal lobes without harming them much at all.
So, if you were gonna play the trope to its fullest, you really should be trying to destroy the head (or sever it, which is probably easier), not just deal a wound that's strong enough to down a real human being.
And, of course, the number one rule of zombie-fighting is to keep your distance, so reach is good, too.
Conclusion: polearms with sharp bits are the best choice of melee weapon. A kaiser blade or some kind of brush hook would make a decent improvised weapon. The much-joked-about monk's spade is a good actual weapon.
(Many zombie movies, of course, throw in the exploding-head trope common to action movies and video games [http://tvtropes.org/pmwiki/pmwiki.php/Main/YourHeadASplode], in which case shotguns and baseball bats and almost anything else that would normally be enough to seriously wound a human being will cause zombie head explosions. Doing you-have-to-totally-destroy-their-heads zombies without that kinda makes them very unfair.)
-- Alex