Always on board; Jumpers, compass, water bottle, binoculars, half a roll of engineer flagging, fire extinguisher, small tool kit, small first aid kit, extra drive belt.
Off our very local area trip: all the above plus, extra water, snacks, map, bag of tools incl ratchet with lug size socket, spare tire & wheel, fix-a-flat can, plus more serious first aid kit, (tourniquet, blood clotter, trauma dressing, snake kit) fire starter, flashlight, motor oil, space blankets, bug spray, plus, we always leave notes where we're heading and what time to expect our return. Usually, in our area, a firearm of some type. (Never had to be used, but wild hogs can occasionally get aggressive.) Plus, we call home when we've loaded, have exited the woods and on a paved road headed home. Never had any serious issues, thank goodness.
But I really like the checklist posted by Milebyro. I'll be getting a copy made and likely add some "Deep Southern Woods" requirements that his list will remind me about. Huge help. Thanks for posting your check list.