99% of the camping we do is boondocking as I dislike RV parks and refuse to pay for a campsite in my own damn state where I pay taxes...but that is a topic all on it's own.
I am going to list the "extra" stuff I use for boondocking only. I will leave out all the things I take everywhere. Some people seem to have listed the entire contents of their trailer.
Chainsaw for firewood. I always have a couple days worth of firewood in the back of my truck, but it's nice to be able to cut more so we can burn as much as we want. I always bring wood with me so I don't have to buy it on the rare chance I stay in a park with a service. Those places are a ripoff. $15 for a wheelbarrow full of wood? No thanks, I get it where I work for about $20/ton.
A couple of aquatainers for extra water.
A generator for obvious reasons.
Other than that the rest of the stuff we carry pretty much goes everywhere with us.
We live in northwestern Montana and may be hours from civilization and prefer it that way.
I always carry vehicle recovery stuff, tools, basic survival stuff, and plenty of guns & ammo...yes I'm a crazy redneck with a basement full of guns, ammo, and reloading stuff. I like to do a lot of shooting while camping as do my wife and kids.
We travel a few places where we stay in parks/campgrounds close to town. We have had good experiences doing this. Just prefer to boondock.
Sorry, long winded. I have a problem with that sometimes.