With no electronics to distract or entertain the kids, take advantage of the dark and plan a family game night. Pull out a board game, and set up some candles. If you are wary of having candles near a cardboard board, you can also play cards. Gin Rum, 500 Rum or Rummy, Egyptian Rat Screw and Crazy Eights are always popular with children, and many teens or young adults enjoy them, too.
If the storm has blown past but the power is still not back on, you can also go outside and play. Hide and seek, flashlight tag and kick the can are great games for a summer night. Just be careful not to trip over any tree limbs that may have fallen, and warn children from hiding under old oak trees unless you can see that there are no precariously balanced broken branches, or widow makers, hidden in the tree.
If the storm is still raging, you can also play the same games inside. Just be sure that children know the rules so that a creative child does not end up accidentally breaking something in their bid to fit in the perfect hiding place.