My purse always has a travel sized hand sanitizer and a lighter, just in case. I used to always carry a knife (or two). I have a mini compass, but i don't carry it on me. And there's a 50/50 chance i have a pen. (A mini flashlight at the least would be a good idea so you can save your phone battery for emergencies, which is what i keep telling myself, but i still haven't gotten one. Oops.)
Admittedly, not a whole lot there in case of a zombie apocalypse... But i could probably incapacitate one by throwing my work phone at its head. XD And *if* i have that pen, a quick stab to the eye for a quick escape (hopefully).