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The easiest way to destroy a perfectly good speaker is to drive it into distortion. Distortion is basically when the speaker emits sounds that are not part of the program material being played through them. There are two main types of distortion: mechanical distortion (like voice coil rub) and electrical distortion (such as amplifier clipping, and ground loops).
Any amplifier asked to play at 80 to 90 % of its potential power will clip and, if given time, destroy speakers. A normal amplifier output signal looks like a sine wave (the peaks and troughs of the wave are smooth and equal). When an amplifier is driven into clipping, the peaks and troughs are chopped off creating massive current surges that feed the speakers. The sound quality of a clipped signal is noticeably worse than a 'clean' signal.
*If you can't get the volume you want from your system you either need more power or more efficient speakers.