When apples are plentiful, imaginations are flagging, and you have at least 8 people, here’s an old-time relay game (careful with those paring knives! Maybe give younger children the eating role, or use safer vegetable peelers):

Form teams of four. Give the first person on each team an apple and a paring knife. First person peels the apple, second person quarters it, third person cuts out the core from each quarter, and the fourth eats the apple. Number Four is not to start eating until the core is cut from all four quarters. The quartet first finished win for their group.

(from The modern Handbook for Girls by Olive Richards Landers, 1933)

A second peeling game requires each player to try to peel an apple in one long strip, as shown above. The longest strip wins.

If you prefer an apple game that involves no sharp objects, how about an apple relay? Each team member races to a designated spot and back while balancing an apple on the back of his hand, then places it on the back of the hand of the next player. If the apple falls, the player has to stop and put it back on and continue the race from where he left off. First team to finish wins.

Or how about pass-the-apple? Players gather in a circle. Each player places his hands on his shoulders and grasps the apple with his elbows (the first player may need help with this!). The apple is then passed from player to player around the circle, using only the elbows. Any player who drops the apple is eliminated. Last player left is the winner.