The following items cannot be taken with you in your carry-on bags, and must be checked in. According to answers on Quora, you can't just check a small item in with the airline without a big box that will travel as a checked in luggage. A big box will ensure that the item is not lost along the way, as it makes its way along the conveyor belts with the rest of passenger luggage.

A knife is allowed only in checked-in baggage. If you have a surgical blade or xacto blade folding knife, you can surrender the blade at security check without surrendering the rest of your knife.
https://www.reddit.com/r/self/comments/3angy2/i_just_went_through_airport_security_with_an.

Not allowed.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/co2-cartridge

Not allowed in carry-on luggage and may not be allowed at destination.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/firearms
https://www.tsa.gov/travel/transporting-firearms-and-ammunition

Also not allowed are compressed air guns.
https://www.tsa.gov/travel/security-screening/whatcanibring/firearms

Not allowed in carry-on luggage.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/bows-and-arrows
https://www.tsa.gov/travel/security-screening/whatcanibring/items/slingshots

https://www.tsa.gov/travel/security-screening/whatcanibring/items/drills-and-drill-bits
What about EDC manual drills under 7 inches? I don't know.
Even screwdriver bits can be confiscated because they can be viewed as drill bits. Although some multi-tools with bits are supposedly “TSA approved”. Maybe smaller 4mm bits are not considered drill bits? I contacted TSA, but they didn't answer the question.
https://brentlogan.com/2011/07/tsas-prohibited-items

Allowed but must not smell of fuel or even have any residue.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/camp-stoves

My alcohol stove doesn't even look like a stove, and if you separate the different parts you will probably be ok. Though the following article states otherwise.
https://www.backpacker.com/skills/stoves-on-a-plane

Any tools under seven inches long, regardless of having a pointy end or not.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/tools
https://www.tsa.gov/travel/security-screening/whatcanibring/items/multi-tools

Lithium batteries within devices, and one or two spare lithium batteries are allowed with certain restrictions.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/lithium-batteries-100-watt-hours-or-less-device
https://www.tsa.gov/travel/security-screening/whatcanibring/items/lithium-batteries-more-100-watt-hours

Scissors with blades under 4 inches long are ok.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/scissors

Must be accompanied with medication, preferably labelled.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/unused-syringes

Matches are allowed as long as they are not “strike anywhere” matches, whatever that means. Apparently the allowed matches come in a book.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/safety-matches
https://backpackinglight.com/forums/topic/42668

As long as it doesn't smell like fuel, car parts are allowed. I wonder what you could bring along that would pass as a car part?
https://www.tsa.gov/travel/security-screening/whatcanibring/items/car-parts

Lighters, except for torch lighters, are allowed as carry on for some reason: https://www.tsa.gov/travel/security-screening/whatcanibring/items/disposable-and-zippo-lighters.
There were smokers with power able to change policy and bring a dangerous article on board. Policy is more about politics than safety.

Disposable razors are fine, but not straight razors or blades.

Corkscrews with no blade are allowed.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/corkscrews-no-blade

Knitting and sewing needles and crochet hooks are allowed.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/sewing-needles
https://www.tsa.gov/travel/security-screening/whatcanibring/items/crochet-hooks

A telescoping fishing pole can be taken with carry on luggage, and you can take some small hooks as well.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/small-fishing-lures

https://www.tsa.gov/travel/security-screening/whatcanibring/items/harry-potter-wand

https://www.tsa.gov/travel/security-screening/whatcanibring/items/light-saber

Nail clippers with a metal file are not allowed, but they will not see the file in the x ray machine, and will likely not care to check for the file.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/nail-clippers

Image search on Google. There are also some multi-tools shaped as keys that have a knife.

A wire saw seems to get past security: https://bushcraftusa.com/forum/threads/small-tsa-proof-survival-kit-land-and-sea.22031
https://www.tsa.gov/travel/security-screening/whatcanibring/items/saws

Pro tip: Ethanol is not denatured in countries whose population is not micromanaged.

You can probably take along 95% ethanol fuel if you spread it into a couple 100ml bottles, despite that the regulation is that only up to 70% alcohol is allowed (in unopened retail packaging).
Due to efficient use and supplementing with firewood, I rarely need more than 200ml. Any and all bottles you take must fit inside a single one liter bag.
https://www.tsa.gov/travel/security-screening/whatcanibring/items/alcoholic-beverages
https://www.tsa.gov/travel/frequently-asked-questions/what-3-1-1-liquids-rule

Any food is allowed on the plane, but your destination city may not allow certain foods through customs. Anything manufacturer sealed in packaging with a label is likely ok.

These are fine for TSA, but if in large quantity check with customs in destination country.
https://www.tsa.gov/travel/travel-tips/can-you-pack-your-meds-pill-case-and-more-questions-answered

If you are traveling with luggage for activities in addition to off-the-grid backpacking, you can put extra stuff in storage at many airports:
https://virtualwayfarer.com/international-airports-and-luggage-storage-short-and-long-term/

More info here