An example of resonance

One of the most famous examples of a structure which was NOT designed correctly is the Tacoma Narrows Bridge, which was dedicated on July 1, 1940. At the time, it was the third-longest bridge in the world.

Alas, it had a strong response to frequencies of a few tenths of a Hz, which were on occasion supplied by winds blowing down the river's channel. Locals quickly nicknamed the bridge "Galloping Gertie" after its gentle swaying. On November 7, 1940, however, a violent windstorm excited very large amplitudes of motion ...

Click the picture to see a movie of the disaster

For more information

The Washington State DOT page on (a new) Tacoma Narrows Bridge
Wikipedia's page on the Tacoma Narrows Bridge will give you some good references for further reading.
"Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks" (PDF) is a paper which claims that the particular resonance set up in the Tacoma Narrows Bridge was more complex than usually described.
Earthquakes can cause especially large damage to structures with resonance frequences close the frequency of the quake's waves. This footage of the earthquake in Kobe, Japan in 1995 allows you to estimate the frequency of earthquake waves.