At the time it opened for traffic in 1940, the Tacoma Narrows Bridge was the third longest suspension bridge in the world. It was promptly nicknamed "Galloping Gertie," due to its behavior in wind. Not only did the deck sway sideways, but vertical undulations also appeared in quite moderate winds. Drivers of cars reported that vehicles ahead of them would completely disappear and reappear from view several times as they crossed the bridge. Attempts were made to stabilize the structure with cables and hydraulic buffers, but they were unsuccessful. On November 7, 1940, only four months after it opened, the Tacoma Narrows Bridge collapsed in a wind of 42 mph -- even though the structure was designed to withstand winds of up to 120 mph.
The failure came as a severe shock to the engineering community. Why did a great span, more than half a mile in length and weighing tens of thousands of tons, spring to life in a relatively light wind? And how did slow, steady, and comparatively harmless motions suddenly become transformed into a catastrophic force? To answer these questions engineers began applying the science of aerodynamics to bridge designs. Technical experts still disagree on the exact cause of the bridge's destruction, but most agree the collapse had something to do with a complex phenomenon called resonance: the same force that can cause a soprano's voice to shatter a glass.
Today, wind tunnel testing of bridge designs is mandatory. As for the Tacoma Narrows bridge, reconstruction began in 1949. The new bridge is wider, has deep stiffening trusses under the roadway and even sports a slender gap down the middle -- all to dampen the effect of the wind.
(Taken from Nova Online: Super Bridge: Suspension Bridges. Also see Wikipedia: Tacoma Narrows Bridge: )
You can view short films of the bridge's oscillation and collapse.