Burger Chef’s signature item and top-seller (until the company collapsed in 1996) was the Big Shef, a double flame-cooked beef patty with American cheese, lettuce and the chain’s secret sauce.

These are the most popular restaurant chains, broken down by generation—baby boomers, Gen Xers, and millennials.

Established in 1960 in Greenville, North Carolina, Hardee’s quickly gained popularity for its charbroiled burgers and biscuits. The chain merged with Carl’s Jr. in the ‘90s under the parent ...