Oh my God, no. No regular zombie apocalypses, no "I'm trapped in one area and I gotta get out" games, -NO-. You wanna do something we don't normally see with Zombies? Let us -be- the zombie. Show me what happens -after- I'm doomed to a life of shambling after my delicious friends and family. All hope is officially lost, I am not fighting the undead horde, I AM THE HORDE.
Or hell, even if you just have a game where it starts with me being bitten. I'm infected, I'm going to become a monster, there is NO salvation (within sight at least) and now I have to decide what to do with my remaining time. Use it wisely, and you go down in history as a badass. Use it poorly ... you chomp down on your buddies before becoming chainsaw fodder.