We live in town, and don't really have one -- we have bandaids, ace bandages, and standard NSaids lying around the house, ditto one or two kids' meds (think fever reducer) and a thermometer. Somewhere we have tweezers, and I did actually recently buy a hand-held mirror (didn't have one) to deal with those "dammit is that a tick on my back" moments when I'm the only one home. We don't really replace anything, though we will replace expired meds if/when we notice they are expired -- particularly if by more than a year.
In all honesty, the likelihood of our having a medical emergency here that (a) requires first aid but (b) does not require professional assistance and (c) includes circumstances where no one's available to drive to the nearby drugstore (or it's closed) and that would (d) matter if we waited 8 hours before getting things taken care of are slim.
We do camp, and for that I care about keeping the above items handy, plus ginger ale and/or apple juice and crackers, because once or twice DS has had a bug while we're camping in a way that those are about all he can keep down/eat. And having a dehydrated kid out in the middle of nowhere would be, while not a total crisis (we're still not in Death Valley, or, say, rural Romania), a potentially more serious problem, so would prefer to avoid it.
We're not users of neosporin, much (though we do occasionally). More a fan of soap + water.