I have done a lot of wheeling in my time, in fact I grew up wheeling vehicles in one from or another and have never carried most of the stuff everyone list on here as part of my regular setup. Number one, my main tool is to always carry another vehicle. I never wheel by myself because that can be dangerous. What I do carry is the normal "get me unstuck" stuff, - tow strap (not snatch chains because they will break and do serious damage to the vehicle or by-standards) Snatch blocks and tree savers for the winch.
If I do carry tools its for quick replacement parts, stuff to change a alternator and belts, because anything else will normally require more work than I am willing to do in the woods, or will require serious replacement parts, because who carries CV shafts, Driveshafts, fuel pumps, water pumps, on a daily basis. Don't lie and say you do when we all know you don't. So when these parts do break, I will need a lift to the store, and can pick up the tools to do the work with while grabbing the parts.