There are a number of reasons.
First, to blatantly steal a line from Warhammer 40k - They are without number, they are without mercy and they are without fear.
Second, it preys on the fear that at some point we might not be in control of our actions. No one wants to kill their loved ones (or re-kill their loved ones depending on who is the zombie).
Third, zombies can proved a great social metaphor, and in fact George Ramero seems to believe one can express all the human societal transgressions with zombies, from racism to consumerism.
Fourth, zombies are a sympathetic enemy. They are not evil like most antagonists found in games and movies, they are simply fulfilling their place in the natural order of things.
Finally, zombies generally accompany an apocalyptic scenario. It can be a localized apocalypse (as in Resident Evil) or a world wide one (as in L4D). It's a common video game trope to pit the player against a seemingly unstoppable foe after the fall of humanity has begun. Zombies are a relatively recent break from the usual Evil King/Demonic Invasion/Alien Invasion/Doomsday Cult/Mad Science scenarios we see most frequently