Here's some ideas I have:
BBQ grill - take the legs off it and mount it to a solid surface but with a drip pan underneath to catch the grease. Fed from a large propane tank mounted elsewhere on the trailer
sink/faucet - fed from tank of water, gravity fed, mounted high on the trailer to get some pressure to operate
small refrigerator - the kind popular in dorm rooms, very small but can keep your spoilable food good. If you think this is extraneous, then cooler or mermite only.
popup camping tent on the roof - nothing says "I'm a serious offroad camper because I need a ladder to get in my out-of-the-way tent."
genset - small, no more than 1.5KW. A Honda EU2000i comes to mind, very quiet and will run everything you need in camp. And 100-ft power cord
at least two fuel cans in mounts - suitable fuel for your genset, not your vehicle. Spare fuel for the vehicle should be mounted to the vehicle, not the trailer.
tool chest w/drawers - for when you have to repair something when you get back to camp. Should include handtools, air tools (only if your vehicle has an onboard compressor), and a few power tools (runs off genset)
ice chest/Mermite - gotta have cold drinks. Period. Paragraph.
full kitchen accessories - all the pots, utensils, towels, dishes, fire starting tools, etc.
small electric water pump - sump pump would be good, plus a 50-ft hose. For if you are near a lake and need to recharge the water tank, or take a shower
shower setup - a small shower setup to run off the water tank/pump. Also: depending on how warm or clean you need the water, a built in tankless portable water heater and an inline cartridge filter will take care of those needs.
chainsaw/lopping shears/bolt cutters/etc. - bigger tools for special purposes, as needed
jackstands - a Hi-lift jack or a bottle jack should be in your vehicle, but a couple jackstands and small pieces of 2x10s to put underneath them would be good for camp repairs under the truck instead of hoping the jack fails with you under it.
tarp and camp chairs - portable shade and relaxation
shortwave radio - a TV is too much, but having a shortwave AM/FM radio would be worthwhile to pass camp time or keep in touch with outside world
spare camping stuff - sleeping bags, mats, emergency supplies, flashlight, etc.
safety tools - good size fire extinguisher, spare cellphone or CB radio, wool blanket, flares, first aid kit of decent size, rain ponchos, road atlas, etc.
spare parts and tools for the trailer - truck should have spares and tools for the truck only. Trailer has parts for itself. Spare tire, nuts and bolts, wire for electrical hookups, light bulbs, GAA grease, etc.
That's about all I can think of now. Might add more later.