hmm, how about a SUPER LEXICON OF DOOM!!!!!!
It's a book that contains all information in the world (yes, even a zombie apocalypse survival guide) and it is also capable of smashing in skulls and break most things you drop it at. Locked door? No problem, it has a quick-guide in lock-picking, or you could just drop it on the lock, and it will be obliterated!
Serious choice: a home made "weapon" (the components were never intended to be used as weapons, does that count? =P) all I need is stuff I can find in my home.. It's pretty much a spear, that electrifies anything that touches the blade. (needed: lawnmower blade, source of electrical power, some wires (or whatever works for you), a stick or something, duct tape)
if I can't have that I would chose a water rifle, filled with petrol, and with a lighter attached to it. (or does that count as a home made weapon again?)
if I can't have that either, I'd just choose a good old fashioned long-handled axe... but only if the others are to "weapon"ish.