The single most useful tool you can take to the woods

An ax will do anything a knife will, and a lot more besides. Build a shelter. Butcher a moose. Cut vegetables for dinner. 

It simply isn't possible to find a good ax in the local hardware store. You'll have to sniff around for a quality antique, or spend some serious money and order from the likes of Granfors Bruks in Sweden. Once you've finally acquired an ax worth owning, it takes a long time and a lot of practice to become competent and safe with it. If you're serious about the outdoors, though, both quests are worthwhile and satisfying.  

Pictured above is my Granfors Bruks "Small Forest Ax", the one I use for everything but serious splitting. It seems to have become the standard for bushcrafters. Deservedly so. Despite being small and light it's remarkably powerful, mostly due to the quality of the steel. It will take as sharp an edge as any of my knives.

I use a few layers of duct tape to protect handles from overstrikes. I've developed enough control that I haven't damaged a handle in a long time. But no matter how zealously I guard my ax, on almost every group campout I attend some kid (or worse, a well-meaning friend) will get his hands on it and take a few whacks.

On the day this photo was taken, I used it to cut and limb a spruce tent pole, then to cut, carve and hammer in some tent pegs. I split more than enough birch firewood for our stay, then further split some of that into kindling. That was the work of minutes, so I selected some nicely-grained billets and carved a couple spoons and a spatula. The bowls of the spoons were dished out with an Indian-style crooked knife, but the rest of them (and the spatula in it's entirety) were carved with the ax. 

For carving, you can choke up on the handle, or even grip the poll and use it like an Eskimo ulu. With a little practice, you'll be surprised at how precise you can be, and how much faster it is than carving with a knife. 

By the way, have at least a rudimentary first aid kit along whenever you're going to do ax work. It would only take an instant to either lengthen or shorten your toes. And stay aware of the "rule of follow-through" - mind the arc that blade will take if it glances off a knot. The shorter an ax, the more dangerous it is.