BUENOS AIRES — As Concepción Martínez, her husband and two daughters pulled into the last subway station here, cheers and clapping erupted from the throngs of people, some wearing turn-of-the-20th-century dress, waiting on the platform.

Camera flashes lighted the tunnels as passengers took their final rides in the saloonlike wagons — with their wooden benches, frosted glass lamps and manually operated brass doors — of South America’s first subway line.

“Every day, I ride this train into work, so this is a kind of goodbye,” Ms. Martínez said.

The antique Belgian-built cars, a symbol of Buenos Aires’s early-20th-century wealth, were taken out of service this year, and their retirement is a poignant example of the city’s struggle to preserve its physical history as some of its icons and infrastructure crumble....