Rope and Cordage
Something a good woodsman will never be without is some good rope or cordage. The two items I will always have one or the other of is 550 cord and bank line. Both of these are multipurpose items that can be used for lots of different things. Constructing a shelter using all natural materials can be strengthened by securing your poles together and makes for a more durable and longer lasting abode.
Making weapons, utensils, or other camp items such as fire tongs can be made improved by having a hank of cordage. With either 550 cord or bank line, you have a fishing line you can use to get yourself calories. Both 550 cord and bank line are also good for making primitive traps. I prefer to use bank line as it is very strong and holds a knot better.
You'll also find snare wire which is excellent for trapping small game. A squirrel pole can be made using this brass wire. Squirrels will take the easiest route to getting up a tree and if you have a pole leaned up against their tree, they will usually take the route.