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There's two easy ways to kill a speaker: using too much power and using too little power. When faced with too little power, a speaker will strain to produce the signal that it's fed. The low-powered amplifier is driven into clipping when the distorted signal reaches the speaker (you can actually hear the clipped-off, 'square' wave). The audible distortion will be noticeably harsh; the highs will sound brassy, the lows will sound muddled. Not only will you blow speakers with this, but you can overload the amplifier and destroy it in the process.
If you're audio system is not producing the sound level, or sound pressure level (SPL for short) you want, it's time to re-evaluate your loudspeaker, and amplifier choices. The easiest way to make a system louder is to get a bigger amplifier. Nowadays, most audio loudspeakers range from 85 to 92 db in efficiency. Some horn-loaded speaker designs can reach efficiency levels of 98 to 105 db. A loudspeaker with this type of efficiency only needs 1 to 10 watts of power to reach maximum SPL's.