Zombies are a very frequent occurence in dreams, me and my friends had so many of them. It's very hard to attach meaning to this since it's so open to interprettation. But I'm beginning to suspect that from psychological point of view it can be interpretted as "me versus the world" scenarios. Where the world is these violent, mindless, irrational zombies out to get us and we / us are the self which we need to protect.
Though, as far as dreams go, I believe that they are just virtual scenario recreations (like in the matrix) with function to drive a response. This can be explained in way, if someone pissed you off during the day and you felt like ripping their head off, but couldn't for obvious reasons, the dream will come and give you that opportunity to release the suppressed emotion. This could be one reason why violent dreams are repeated often.
Don't cry, don't regret and don't blame
Weak find the whip, willing find freedom
Towards the sun, carry your name
In warm hands you are given
Ask the wind for the way
Uncertainty's gone, your path will unravel
Accept all as it is and do not blame
God or the Devil
~Born to Live - Mavrik~