... it is possible to generate a sound wave of the right frequency and amplitude to set a glass vibrating at a constant rate without it breaking. It is also possible, and if you've never tried it, quite easy to make a glass produce a note because of the same phenomenon. Lick your finger and run it around the rim of glass. Start slowly and with a light pressure. Carefully increase speed and pressure until it produces a note. Maintain that speed and pressure and the glass will continue to "sing". Lift your finger and the note will continue momentarily, decaying as the glass returns to its stable state.
If one were to look at a super slow motion video of the glass one would see the glass "rippling" with the vibrations. I'll try to track down a video clip ... there's just got to be one on youtube!