For their important little bits and pieces 
We have a plastic lidded box that lives under a chair. Over the years various pig paraphenalia has found its way in.
Most things can be found on Amazon or Petshops, some in chemists. Keep an eye on use-by dates but better to have them than wait till you need them:
So:
syringes for feeding little unwell animals. We bought some big 20ml ones, our vet gave us some insulin syringes (in 0.1ml increments) and I have a couple of the Calpol syringes.
Critical Care fine grind (or in an emergency , mashed up pellets sloppy to syringe feed)
Probiotic powder with Vit C (goes onto veg)
Small scissors to trim things like fur knots, or from a wound
Tweezers to remove stuck things from teeth (grass,hay)
Clean non fluffy gauze to cleanse with salted water (boiled and cooled) , good for cleaning up wounds or taking seeds or hay out of piggie eyes
Their claw clippers ( best ones I've found are like a pair of scissors with a round 'notch'. The claw needs to be cut clean, not crushed, I also use a pair of finer clippers for the pinkie claws that curl in.
Shampoos- we used to use "Just for Boars" when we had the boys, now I have Cedar and Lemongrass. There are conditioning shampoos for long coated pigs.
Calendula cream (healing) for little dry bits
Xeno 450 drops - mites, lice , worms
Vit C tablets to crush and syringe feed if needed
Vaseline as a protector for any little scratches, stops them niggling them
Virkon S to disinfect the Pighouse if I introduce a new piggie (I also use a steamer if I just want to clean it) white vinegar to remove pee stains
their staple remover for newspapers
The Vets details.
A child's sock , in case they need to be a SockPig (there was a piggie who needed to be a SockPig to stop her scratching. They don't DO bandages and plasters)
Some things I rarely use but it's reassuring to have things where I need them.