In brief
Pack to the weight budget first, not the wish list. Everything you bring comes out of the payload, and every high, heavy item changes the way the rig handles. The equipment that pays for itself is the equipment that prevents damage or solves a problem in the field: a water hose, a waste water hose, a spirit level and a set of wedges, a spare belt, a decent first-aid kit.
The essentials, and nothing negotiable
For a caravan: a properly rated hitch, safety chains crossed, a breakaway lanyard, a 7-pin or 12-pin lighting socket, wheel chocks, a jack and a spare wheel. For any rig: a fire extinguisher, a smoke alarm and a carbon monoxide alarm with recent test dates, a spirit level, a set of levelling wedges, a water hose with a pressure regulator, a waste water hose, and a torch that is genuinely bright.
Comfort that is worth the extra weight
A good camp chair and a table you can actually use for dinner are the two items that change the quality of a trip more than anything else on this list. A folding water container and a way to fill it solves the problem of arriving with a nearly empty tank. A kettle that runs on the same gas as your cooker saves you waiting for a mains socket. And a decent blanket matters more than any gadget in a cold month.
Usually regretted
Half a wardrobe, a full crockery set, an iron, a large television and every small appliance you can plug in, because in most systems there is not enough power to run them all at once. Weigh the ones you are tempted by before they go in.
Regional extras (what each region adds)
In cold countries, an insulation kit for the fresh tank and the pipes plus a heating source with a timer. On alpine routes, snow chains and an idea of when they go on. In desert and outback regions, far more water than seems reasonable, a serious sun shade, and a way to recover if you get stuck. On islands and on ferry routes, a booking confirmation for the vehicle and a printed copy of any permit.