The only thing we rely on for emergencies is the vets phone number (which is on my mobile and on the vets business card which I keep in my wallet) and the hams pre-prepared carriers which always have susbtrate and bedding in them ready to get the ham out in a hurry if needed. We also have a carrier for the mice that we keep ready. That way if there is an emergency we can just put the pet in their carrier and get going - my OH can ring the vets while I drive if it comes to it.
We do have other things around though
We have...
Baby nail clippers for ham claws
A stypic pencil incase a claw gets cut too low when clipping
Keto-diastix and multistix
Digital scales (that weigh to 1g)
Dr Squiggles
Snugglesafe
Probiotics
Needle-less syringes
Smaller cages if needed as hospital cages
Rocks/ceramic toys (can go with the ham to the vet on a hot day)
Two old blouses for covering carriers to give shade in the car or to help protect them from the worst of the weather
Larger fabric dog/cat carriers for if we need to take more than two carriers somewhere
Tea tree cream
Frozen veg (means we always have veg avaliable if a ham needs the vet)
Hamsterlopaedia
Clean jars for health checking less tame pets
Cotton buds
And currently metacam cause a ham is on it, ronoxan cause a ham is on it, baytril cause the mice were on it until recently, and a few other meds we should return to the vets for disposal cause we don't need them around now.
Oh and I have a fairly well stocked human first aid kit, which we can use for the hams if we need it but thats unlikely.