I have a small Stanley toolkit box in the boot. It always has:
Torch
Work gloves
2 pairs disposable gloves
Smallest size Ikea Ziploc bag with mini 1st aid kit (few antiseptic wipes, band aids, 1 bandage and pins, 1 emergency foil blanket)
WD40
2 straps for tieing things to the roof (not my idea, they "appeared" courstesy of DH)
2 pocket packs of tissues
2 rechargeable handwarmers (the kind you boil up to recharge)
2 mini bags haribo jellies (I used to have cereal bars, but DD keeps eating them all).
I also have a bag of shopping bags there too.
And a proper kit to change tyre, including the stuff to blow up a tyre in a can, and a pump to inflate with air, under boot carpet
In the car, I have hand sanitiser, disposable gloves, pocket pack tissues, nail file, pen and notepad (one from beside a hotel phone), bag of change for parking meters etc, painkillers, bag of sucking sweets (currently werthers, often fruit flavoured boiled sweets or mints), and window scraper.
I keep meaning to put bottles of water and cereal bars or similar back in - whenever I do, they get used up very fast! And wet wipes also need replacing as DD left the current pack open and they dried out.
I usually also have sunscreen there in summer too.
When DD was smaller, I always had a pencilcase filled with crayons (not pencils as can't pare them when driving) and a small colouring book or notepads for her, and we used to also have a dvd player as we had a lot of long distance driving to do. And a CD of children's songs to sing along with. (And some audiobook stories on CD sometimes as well). The multipacks of small boxes of raisins are also useful for car door pockets when small DCs are involved...
I usually have my work bag in the car with me, and that has a small pouch containing emergency san pro and spare underwear, which has been helpful once or twice over the years. And that also has my asthma inhaler, so I don't worry about a spare in the car generally.