Not a hunter, but I carry a small collection of survival items any time I do anything in the woods.
The mainstays in my kit are:
Fire kit (Tinder, and at keast 2 sources of ignition (lighter, matches, ferro rod, fresnel lens... I usually carry 4+ sources actually)
Emergency shelter (I use an AMK 2 person heetsheets blanket)
Repair kit (duct tape, tenacious tape, needles, dental floss, thread)
Some way of purifying water (whether that be boiling, filtering, or using drops/tablets)
Small roll of cordage
Knife, obviously
That might be it for a day jaunt on marked trails. I may add more items like a compass, etc...