Most in the ultralight backpacking community eschew a knife, although I think doing so is folly.
For a long time I carried a Gerber Ultralight LST, which did everything I needed it to do at the office, in the car, and at home (where bigger knives were readily available if needed). I felt the ULST was more than adequate for outdoor endeavors, but one weekend I ventured into a temperate rainforest and realized my little Gerber was nowhere near up to the job of processing kindling in the wet environment if such activity was required. Fortunately, I was using an alcohol stove so had no need for a fire, but it was all too apparent that getting soaked could quickly foster such a need.
When I returned home from this outing I embarked on a search for a small fixed blade knife that was capable of batoning without weighing too much. I opted for a Bark River Mini Fox River with a stout, 2.9-inch, 3V blade. At 3.9 oz it's not ultralight, but it does provide great utility and insurance.
Given a knife is considered one of the outdoors 10 essentials, I recommend carrying a small fixed blade knife into the bush for anything more than a casual day hike. Take a look at the ESEE Izula.