From gangster getaway cars and the Batmobile to the humble family sedan, the basic three-box configuration of a passenger car—low engine compartment, higher cabin, low trunk in the rear—has endured for decades as the standard shape of the automobile.

Until now. Sedans, long a symbol of the American open road, are fading in the rearview mirror. In an industry-altering shift, millions of drivers have made what seems to be a complete embrace of sport-utility vehicles.

The...