Any ideas for variants for this? I came up with a simple "weapon" system today - if you pass certain pre-decided bits of scenery ("vehicles and shopfronts that might contain a useful weapon" seemed to work), you gain a weapon which you can use to take out one zombie. It instantly added more depth to it - within ten minutes I happened across a couple of police cars parked on the other side of a busy street, but with a lot of shoppers using that pavement.
Could maybe go for a two-hit "life" system, with a way to restore your life if you can find the right scenery before another zombie gets you. And was thinking about something that lets you walk through the zombie horde without them noticing you, for a limited period of time, but couldn't think of anything to tie it to thematically.