IN my atv all I keep is fuel and oil, and in trunk a small air compressor and plug kit
ON my atv, however I tend to carry just the basic's in a small tool kit that mounts to my fuel tank cap, had a bag on both sides that is zippered closed, NOT water proof, but I keep things in it in waterproof bags, and remove bag when towing in /on an open trailer, or when left outside! (it its mostly always kept indoors and a enclosed trailer)
basic hand tools, vice grips two sizes, zip ties, folding hand saw, assorted zip ties, electrical tape, a small flash light, two ratchet straps a lighter, some TP, a few wet wipes, a bottle of water, and a small first aid kit,
and in a separate bag that mounts to my rack, IF going far or on more adventurous ride, the winch bag, that has a snatch block, a few d ring's, a tree saver and a tow strap, and a two pair of gloves.
a lot of what all I carry really comes down to where I plan on going and how long I expect to be gone, I tend to over pack I thiunk, but like a boy scout, I'd rather have it and not need it than need it and not have it when far off and a LONG walk out area!