Varieties

There are actually three different kinds of zombies. All of them are like humans in some ways, and all of them are lacking something crucial (something different in each case).

Hollywood zombies. These are found in zombie B-movies. Their defining feature is that they are dead, but "reanimated". They are typically rather mean, and fond of human flesh. The zombies pictured on this page are mostly Hollywood zombies (though I'm informed that the one at the bottom is really a ghost demon). An expert tells me that the name should be "Pittsburgh zombies", since the most important zombie movies were made in Pittsburgh, but somehow it doesn't have the same ring.
Haitian zombies. These are found in the voodoo (or vodou) tradition in Haiti. Their defining feature seems to be that they lack free will, and perhaps lack a soul. Haitian zombies were once normal people, but underwent zombification by a "bokor" through spell or potion, and are afterwards used as slaves.
Philosophical zombies. These are found in philosophical articles on consciousness. Their defining features is that they lack conscious experience, but are behaviorally (and often physically) identical to normal humans.