Knives I like:
Victorinox Trekker: heavy compared to most ultralight gear, BUT, on the survival side, a very handy tool. It has a 3.5" locking blade, a saw, can opener, bottle opener, large flat locking screwdriver, awl, and phillips head, as well as the usual tweezers and toothpick. The price is good too-- $25-$35 Ebay or on-line vendors. Victorinox makes another large frame model, the Outrider that has a similar tool set with the addition of scissors, weighs more and and costs more like $35, and is harder to find.
Swiss Army knives in general are cheap and you can find just about any combination of tools you want. A blade, awl, and scissors top my list of wants for field repairs. The little Victorinox Classic is a great grooming tool and fine for small repairs, but, as with the Leatherman Micra, I would pair it with a larger fixed blade for all round coverage. The Classic works great on a neck lanyard too.
I found when looking at knife options, and geting hung up on scissors, I could add a pair of Fiskars embroidery scissors for less than an ounce. And I got them at a flea market for $2. They have far more utility than any multi-tool scissors.
Frosts of Sweden and Eriksson mora knives. Fixed blade Swedish work knives that are dirt cheap and light-- about 3.5oz with sheath for a 4" stainless mora and I paid a whopping $7.90 for it at a commercial fishing supply. The Mora 2000 is a larger and more expensive model if you have Rambo stirrings and want a bigger knife.
Buck Hartsook. This is a tiny neck knife (it is worn on a neck lanyard). 0.5oz without the sheath, S30V steel, about $30. This is a perfect tool to have with you all the time, on a lanyard with a micro LED light, a firesteel and a backup keychain compass. It's about the size of your forefinger and I think it is the ultimate ultralight dilettante's knife. Yes, I have one :)
There is a long tradition of neck knives for outdoorsmen and the tradition continues. They tend to be small and light and meant for utility. That's a prefect criteria for ultralight hiking. I mentioned the Buck Hartsook, but it's a little small. AG Russell sells a knife called a Woodswalker (see http://www.agrussell.com/customer_appreciation/fixed_blade_knives/a_g_russell_woodswalker_in_leather_hip_pocket_sheath.html) that is basically a heavy duty paring knive. It is 1.2oz and sells for just $20 with a Kydex sheath and neck chain. Becker Knife and Tool designs were being produced by Camillus, who just went bankrupt. They made a neck knife called a Becker Necker that is a perfect knife for hiking. You can still find a few for sale. Columbia River Knife and Tool offers a couple neck knife models. They are inexpensive, but the steel is inferior. I would buy a Swiss Army knife first.
Boker Subcom and Trance. These two knives were both designed by Chad Los Banos and share look and feel. Reasonably light, great utility and low cost. I carry the Trance as my everyday pocket knife. They have a good flat profile and good quality stainless steel.
Multi-tools have their uses. The Leatherman Micra is a great tool and has good horsepower for the weight, but I see it as an accessory to a larger knife if really heading into the backcountry alone. A Micra and a mora make a perfect pair. From the Micra and other small multi's, the weight jumps up to about 6oz (Gerber 400) and there are others that break the 12oz mark. I can hear those with a 5 pound base weight screaming outrage at the mention of a 12oz tool :)
If you want a really big cheap knife that can be abused without guilt, the Cold Steel Bushman is the one to get. It has a handle like a shovel socket and can be turned into a spear. Destruction tests prove it to be tougher than some $300 tool steel Rambo monster knives. It can be used to baton firewood and shelter poles in a survival situation. This is a knife you can dig a hole with and then sharpen it with a smooth stone! Not an ultralight, but light for its size.
Paring knives. If you want a good cheap lightweight knife, you may need to go no further than your kitchen. Paring knives have blades in the 3"-3.5" range and can be found in stainless and carbon steel. Finding or making a sheath will be the biggest challenge. Victorinox makes a stainless steel serrated paring knife that is used by commercial fishermen for a utility knife. The cost about $3 and weigh less than an ounce. The blades are thin and flexible, so they aren't a good heavy cutting knife, but they will shure take care of your camp chores-- add a Victorinox Classic or a Micra and go. They come with a plastic envelope that is adequate if you carry it in your cook kit or you can buy cordura or kydex belt sheaths for them too.