I don't carry a full tool kit most of the time. When I'm going far from pavement - I have a tool bag that includes most of what was already said above

The regular wrenches, screw drivers, pliers, etc.

What I also keep along that might be useful is:

Lighter
rescue tape - yeah it's $10 for a little roll, but it is pretty handy if you need it.
Duct tape (small roll)
Spool of spare wire. I keep some ~10ga wire. About 20 feet. Plus a few crimp ends. And a wire pliers.
Spark plug socket

I usually take my 20v impact and 20v angle grinder with two full batteries. Impact for faster trail repairs. Angle grinder for cutting whatever needs cutting that I can't do otherwise - like a skid plate that's damaged, cutting off a damaged bolt head, a crushed exhaust tube, or ?? I have used it to cut off the teeth on a transfer case output shaft in the most in depth trail repair I've been around. Broken 4:1 output, only had a 2.3: output spare, so they used my grinder and cutoff disc to cut all the low range teeth off the 2.3 output shaft so it would work in 1:1 high range with the other shaft. - just an example of something you can do with an angle grinder that would be very very hard to do any other way.

roll of electrical tape

I think that mostly covers what I carry in my tool bag.

I also have a second bag of off road recovery and communications gear that I keep together and put in when I'm going to remote areas. In that bag is:

Tree strap
Snatch strap
D shackles
Hitch skid plate
CB radio
Ham Radio
Gloves
extra hitch pin
punch (for repairing damaged synthetic winch rope - I ended up pinch cutting my winch rope two weeks ago in moab on an approach to a steep rock face - pinched the rope between the fairlead and the rocks. Doing a brumel splice is super easy, but only if you have something like a punch to use to guide the rope through. I didn't have one. A sharpie marker was what I ended up using.)

I always carry a survival bag with a few items:
mini camping stove set (jetboil style - cheap $20 amazon version) - this is just handy for hot chocolate at the trail head or coffee or whatever.
about 4 MREs
Rolled up blanket.
Trail repair canvas tarp (for laying on in the dirt - thanks to slee offroad! for the swag)
First Aid Kit - I have an Outer Limits Supply kit. It's big, but very complete.
A gallon of water
Extra sun screen
Jumper battery kit
Air Compressor and hand tools - valve stem remover, spare valve stem complete, and gauge- I also have some easy air down things - but I never use them. It's easier/faster to just pop the valve cores and let the air out manually.
Handheld Ham Radio - I keep a handheld Baofang HAM in my vehicle and my wifes all the time pre-set to a specific channel so we can communicate in the event of a natural disaster/emergency if cell service is out.
fire extinguisher.

I think that covers what I carry in my tool kits. Most of which I leave at home 99% of the time.