One thing people seem to never appreciate is rope. Even if it's just ten or twelve feet in length, being able to tie a gate shut or a door is sometimes a life saver. You can use it like a trap, tripping zombies for easier kills, or you can use it to tie up your stuff. You can also use it to lose some weight on a climb, then haul your stuff up afterwards. The best kind I've found is the stuff they use for rappelling. It's strong, lightweight, and you can carry a lot without sacrificing too much space. If you're creative, you can use it to trap and contain animals. Finally, you can use it to rig a hammock if you would rather not sleep on the ground in zombie territory.
Lesson? Make sure everything you carry has more than one use.