A pretty traditional Swiss Army knife is what I usually bring.I find the scissors almost as important as the knife and probably more frequently used when I am hiking nowadays. 56 grams (2 oz).
Comments and current insights: There are lots of smaller and lighter knives than the one above, all the way down to a piece of razor blade with some duct tape that protects your fingers. This Swiss Army knife has some accessories that I do not really need, but the tweezers can be useful as well, for taking out splinters. If you travel with fuel, stove and a shelter, which most hikers usually do these days, the need for an edged tool is limited. If you rely on building fires, you need a sturdier knife. More on that in the book.