For anything that requires batteries, either a hand-crank or solar panels to charge it during a long-lasting blackout.

In many minor emergencies, cash can be useful as a backup to any given backup. (And debit or credit cards as a backup to the cash.)

A deck of cards. Keeping up morale (and/or keeping the kids from driving you buggy) can make many near-horrible situations moderately tolerable, and as long as you've got light, cards don't use up any further batteries or other resources.