Essential knives are going to be the ones you need to complete a given task, cover a need, etc. For me, it really depends on the situation. A chore around the house? I would probably say a utility knife - I have one in my garage toolbox, one in my house-bound tool bag, and I even threw a spare into the little tool kit I keep in my car. For me, they are THE knife for boxes, dry wall, clearing hair out of the vacuum cleaner, due to the thinness of the blade, the acute angle of the tip, and the cheap and easily replaceable blades. And, I can change them out with the screwdriver tip on the Vic Classic I keep on my key chain. That's my other essential knife. I don't have much need or use for a knife at work, so that's all I bring. On the off chance I do use it at work, it has been to cut the strap off of a box of printer paper, which saves me the seven seconds it would take to shimmy the strap off of the box. It's small and unassuming, always attached to my keys, covers my bases well (paring knife and small cutting board fit in my lunchbox quite well for anything food related), and if I need heavier scissors, I've taken to carrying a pair of Slip n Snip scissors.
Now, I'm a knife nut. For some reason, I like having a SAK with a saw when I go camping or hiking, a Sodbuster or Opinel AND my Mora when doing yardwork, one of my multitools and my Buck 303 when doing honeydos that involve repairs, fixes, or construction, and a Spyderco PacSalt or my coyote brown Avispa when I want a large, thunky knife. They aren't necessary or essential, and I romanticize the hell out of them, and they're almost never used (except for the MT...I usually grab that things before I know what I'll need; sometimes my Charge TTi does the job, sometimes I need something more useful), but I like them, and feel psychologically reassured when I'm able to carry my pocket jewelry. Not so much that I feel more confidence or reassurance by having any particular knife on me, just for the sake of having it on me, but more like something is right in the world. It's hard to put into words, I suppose. That's my story, and I'm sticking to it.