A robot, six batteries for the robot, a triple charger for the batteries. We also bring a shelf unit, and put spare parts and such on it. We have our traveling toolbox, which is a medium sized chest, with wrenches, screwdrivers, pliers, two cordless drills with batteries and charger and bits, a cordless jig saw and blades, big hammer, files, tin snips, pry bar, rivet gun, hacksaw, small vise that we clamp to the provided table with C clamps. And some other miscellaneous small tools.
Look at what it took to build the robot, think about what things you can fix or upgrade at a competition. Bring the tools needed to do that work.
We go light on spare parts, compared to some teams. We have traveling hardware box, which has a few samples of almost all the fasteners we use to build the robot, plus some other sizes, for just in case. We bring short lengths of aluminum extrusions, and usually some polycarb sheet and some plywood, and a few chunks of wood (they come in handy). We bring a limited amount of electric and pneumatic parts, and usually don’t need any of them, except perhaps some terminals, quick connect fittings, and plastic tube. And maybe a replacement pneumatic cylinder.
Since I usually end up hauling all this stuff, I’ve worked over the years to limit what we bring, but also try to make sure we bring enough.
If you are lucky and have someone willing to bring half your shop with you, then you would probably bring a lot more than we bring.