A friend and I had a conversation at work on what our top 10 essential pieces of cookware would be if we could only have 10 and nothing else. We both ended up bumping it up to 12 because we couldn't part with a few things, but these were my choices, most important of which would be the Chef's Knife and the Wok.

A lot of my picks were because of their versatility, e.g. the wok which can deep fry, saute, boil, and even bake if you're brave enough, or because of their necessity.

Here is my reasoning for each of my picks:
Can Opener: knives can open cans, but I don't want to have to ruin my chef's knife by doing so
Wok: Carbon steel is easy to clean, durable, and non-stick and can still get good color and fond when sauteeing meats. The form factor is more versatile to boil or deep fry, and big enough for soup or stew while still being able to saute. I almost went with a cast iron pan for this pick, but it isn't big enough for soup or stew and doesn't do well with acid.
Chef's Knife: probably the most important tool of all, and the most versatile knife of all the blade choices. You could probably substitute a cleaver here but I am more used to the chef's knife personally.
Chopsticks: I feel like chopsticks are more precise and versatile than tongs or a spatula. This one is more personal preference. (especially because they're so easy to clean).
Corner Spoon: can't use chopsticks for liquids so I picked a corner spoon which can double as a spoon and a spatula.
Cutting Board: probably one of the weaker picks, but I think it's necessary to keep your countertops safe and also to keep your blade from dulling too much with use.
Food Scale: Another important one, you can't recreate recipes accurately without measuring ingredients. Some scales have a liquid and solid option so you will be able to measure both volume and weight close enough to be accurate.
Immersion Blender: probably my weakest entry, but I feel like it's necessary enough to include. You can't make certain things without a blender and the immersion blender is more versatile than a countertop one.
Mixing Bowls: Essential for mise en place and separation of ingredients, for recipe and/or safety.
Mortar and Pestle Necesary for spices and ground ingredients that a chef's knife would be too tedious to use (e.g. ground cumin). More versatile than just a spice grinder.
Thermometer: Essential for accurate cooking temps and food safety. You could technically do it all by feel, but to me especially in the context of baking and meats, accurate temperature is important.
Whisk: Another weaker entry, but you couldn't make things like hollandaise or whipped cream without one. You could probably remove this one if you had a whisk attatchment on the immersion blender.

I did not include heat or cleaning stuff in this list which is technically also necessary. You need some form of heat (like a stovetop or campfire) and refridgeration to cook too, and some cleaning agents.

I'm curious what you all would add, remove, or swap to the list. What's essential to you?