For backpacking, I rely on a tarp/tent for shelter, good clothing and sleep system for warmth and a stove for cooking. In pretty much every place I've backpacked in the lower 48 either ban harvesting of wood for shelter and fires or actively discourage it as a part of a leave no trace ethic of leaving the place visually undisturbed for the next visitors.
For short lightweight trips, I limit my food to stuff that is pre-cut or is packaged to be boiled. I find a small Leatherman PS4 Squirt to be ideal. Scissors are useful for first aid and gear repair. The pliers are useful for repairs, primarily fixing jammed zippers and pushing a heavy needle through webbing. The knife blade is sufficient for opening packaging and cutting cordage (nothing heavier than paracord).
On trips where weight is less of an issue, I may take food that needs to be cut or spread and on such trips, I find that a lightweight folding knife is ideal. I like the Opinel 9 or 10 Inox, but there are tons of decent ones out there. The Buck Bucklite Max Medium, Buck Spitfire/Slimline are light, inexpensive options.
Outdoor Carry by
Pinnah, on Flickr
I started carrying a small folding wood stove for emergency use on winter XC trips and it's found a permenant place in my emergency bag. This gives me a very easy way to maintain a small "scout" fire with minimum needs for wood processing and with minimal impact as it takes very little wood to keep running and leaves very little ash. On trips where I know it will be snowy or very wet, I may swap my Opinel for a Mora Companion. The Companion is more than enough to keep the Emberlit stove running and for me, anything beyond this is just fantasy fullfillment or carrying a knife just because you like it. Both are fine enough reasons if it makes you happy.
Note, I find fixed blades to be a PITA on backpacking trips and much prefer a folding knife that can be easily pocket carried.