RIDGEFIELD PARK, N.J.—People in New Jersey pick their own strawberries. They chop down their own Christmas trees. They check themselves in at airports and check themselves out at supermarkets. Lately, a few New Jerseyans have been wondering whether it isn't about time they were allowed to pump their own gas.

Pumping your own gas is illegal in New Jersey. It has been for 61 years. It's also illegal in Oregon, and in the New York town of Huntington, on Long Island. Just about everywhere else, self-serving Americans do it themselves....