Why does a glass filled with water shatter when you run your finger along the rim of the glass?

A piece of crystal stemware has a natural or resonant frequency that can be excited by rubbing a moistened finger between its rims. Filling the glass with water merely alters the pitch of the tone. The tone you hear is formed when the crystal vibrates at frequencies in the audible range for humans. Although it's hard to see, the glass actually flexes during the vibrations. If the glass deforms sufficiently, it can break, as crystal is brittle and not very elastic. It is not likely that a flawless glass could be made to break merely by rubbing its rim.

The Myth Busters demonstrated the resonance of a crystal glass and shattered some by exciting the glasses with a human voice. One professional singer broke a glass with no the use of amplification. See the video.