LOL, AC. Those homemade piggin strings also make handy gate latches in a pinch. Heck, I've even used one as a neck rope to ride with after my bridle got broke beyond repair.
Aside from the rope and the knife (and common sense, of course ), I really can't think of much else that is a sure enough necessity. There are other things that are nice to have, but none that can't be lived without.