If you ask any good survivalist what one item they would want if placed in a wilderness survival situation, likely all of them would argue a good knife. A good cutting tool helped shaped most civilizations and started with crude objects like flint knives, sharpened bones, rocks, and wood, and eventually became the knives we’re more familiar with today made of metals and hard plastics.
The lightweight backpacker often finds themselves in quite a quandary when deciding which knife to carry while backpacking. Some people who count every ounce often don’t carry one at all assuming they will not need it due to personal knowledge of their environment or the reality that they may be hiking close enough to civilization that a survival situation requiring a knife is irrelevant. For the rest of us, we must make a choices based on experience, environment, and personal comfort, as each may use a knife for different reason (survival, utility, protection, etc.).
There are many lightweight choices for backpackers concerned with counting ounces. Some may seem more practical than others, but it depends on the person. Some choose to go to the extreme of carrying a single razor blade and others have been known to use a single razor from a broadhead (bloodletting arrowhead) attached to something.
Likely one of the most lightweight options is a simple razor such as the Derma Safe Folding Utility Knife (http://www.derma-safe.com/folding-utility-knife.html).
Swiss Army makes a ton of various “multi-tools” which contain at least one cutting blade as well as other options. Many lightweight backpackers seem to prefer the “Classic” (http://www.swissarmyknifemall.com/product/53181-mo) which consists of a cutting blade, nail file, scissors, tooth pick, and tweezers. Ultralighters often cannibalize this knife to obtain only that which they need and to discard other parts which cause unnecessary weight.
Building off the “Classic” model, some prefer one which offers a whistle (http://www.swissarmy.com/MultiTools/Pages/Product.aspx?category=originalswissarmyknives&product=53933&). The pealess whistle does sound, but it isn’t quite as loud as a Fox 40 or other survival whistle.
Still others who like the “Classic” model lean towards having a light source integrated into the system like the “Swisslite” (http://www.swissarmy.com/MultiTools/Pages/Product.aspx?category=originalswissarmyknives&product=53020&).
Others who want something a little heartier lean towards the “Swiss Army Trekker” (http://www.swissarmy.com/MultiTools/Pages/Product.aspx?category=lockblades&product=54854&) which offers a locking blade and a nice saw feature.
For those convinced they need a fixed-blade knife, my recommendation is for the Mora of Sweden line. These knives are made with incredibly hard and durable steel, carbon, or stainless steel and are very low weight compared to others. They are also very inexpensive, usually less than $12.00 (USD). Laminated carbon options, such as the F780 (http://www.bensbackwoods.com/servlet/Detail?no=60) are excellent field knives and hold an edge well, but are subject to problems with moisture. If around moisture, a better option is a stainless steel blade such as the Mora M545 (http://www.bensbackwoods.com/servlet/Detail?no=165). Compared to other more conventional knives which weigh anywhere from 8-12 ounces, these weight around 3.2-3.8oz with their sheath.
Many other people carry genuine "multi-tools" like those made by Leatherman, Gerber, Buck, and others. Although these tools offer a tremendous variety, they come with the cost of weight and therefore aren't often a realistic option to lightweight backpackers. There are many other knife manufacturers which offer better blades, but they too tend to be heavier and fancier than necessary and not really appropriate for prolonged wilderness conditions. Some near tiny options include key chain knives which aren't very stable and don't offer a realistically useful blade for backwoods needs.