Among the games they play, according to an article in the Wall Street Journal and reprinted elsewhere:
10 in 10: Two teams each spend 10 minutes choosing 10 items to put in a shopping cart. The carts are then given to the other team, which must return the items to the shelves where they belong. The first team to finish wins.
Scavenger Hunt: A popular version is known as A-Z; the first player or team to find one item starting with each letter of the alphabet wins.
Aisle Football: This game involves actually tossing a football in the store, so it's not recommended.
Another game mentioned in the WSJ article is "a relay race limbo under the shopping-cart stand."