The walkway was actually the site of a great tragedy a week to the day after the bridge opened.
May 30, 1883 was Memorial Day. Holiday crowds flocked to the bridge, as it afforded spectacular views, being the highest point in either city. A crowd got very tightly packed near the New York end of the bridge, and panic broke out. People began to scream that the bridge was collapsing, and the crowd of holiday revelers stampeded and twelve people were trampled to death. Many more were injured.
The bridge, of course, had been in no danger of collapse. To prove the point, the great showman Phineas T. Barnum led a parade of 21 elephants, including the famous Jumbo, across the bridge a year later, in May 1884. Barnum pronounced the bridge to be very strong.
Over the years the bridge was modernized to accommodate automobiles, and the train tracks were eliminated in the late 1940s. The pedestrian walkway still exists, and it remains a popular destination for tourists, sightseers, and photographers.
And, of course, the bridge's walkway is still quite functional. Iconic news photos were taken on September 11, 2001, when thousands of people used the walkway to flee lower Manhattan as the World Trade Centers burned behind them.