A "must-have" is an item that a person cannot do without. My family has learned over the generations that the only true must-have is kept between your ears where they can't get it. Who "they" are changed several times.
For the world post-collapse there are many must-haves. After all, everything a person needs that they depend on modern society to provide for them will have be made by hand. For me, the postulate I've been basing my work on is "if you can't make it from scratch with what you find on the ground, don't expect to have it." So, this is a list of the must-haves I must-have for the world post-collapse. Please comment and add your own. I'd hate to learn that this list was incomplete five years too late.
1) How to make a fire in all kinds of weather.
2) How to make clothing and shoes.
3) How to make at least one weapon from scratch.
4) How to use that weapon to take down prey.
5) How to skin and otherwise partition that prey.
6) How to cook the animal.
7) How to identify and use a variety of edible plants in the summer and winter months.
8) How to identify and use a variety of medicinal plants, most especially ones that help with cuts and abrasions.
9) How to flintknap (without this you just haven't quite reached the stone age yet), or at least how to fire-harden wood.
10) How to make shelters appropriate for both summer and winter.
Each of these requires a lot of secondary knowledge that is not explicitly listed. For instance, learning how to make fire requires a certain level of knowledge about trees and tree identification. Making most weapons, tools, and clothes would require cordage. Flintknapping requires a rather thorough knowledge of a variety of stones and where to look for them.
Another thing to keep in mind is that this is only the must-haves. The like-to-have and would-be-nice-to-have lists are quite a bit longer. It is quite a bit to learn, but luckily it's all inter-related. Medicinal and edible plants often differ only in the method of delivery, part of the plant, and the amount ingested. Also, flintknapping will help with making those weapons. Depending on the shelter, the skills of making clothes, weapons, or skinning a animal might be relevant.
Ultimately this is only my list, and it is subject to revision. Everyone intending to survive has their own, feel free to share yours.