"Damaging Woofers:
When a woofer is driven with a high powered amplifier to high levels, there will be a significant amount of current flowing through the voice coil. Since the voice coil has resistance, there is a voltage drop across the speaker's voice coil (which the amplifier appreciates greatly

. This means that there may be a great amount of power being dissipated (in the form of heat) in the voice coil. When a speaker is driven with lots of clean power, the cone moves a great deal (in proportion to the output voltage from the amplifier). For speakers with vented pole pieces (or other types of venting), this movement forces a lot of air to flow in the magnetic gap (area where the voice coil rides). When the woofer moves out of the basket, the chamber that's under the dust cap and around the voice coil expands (increases in volume) which pulls cool air into the magnetic gap. When the woofer moves the other direction, the chamber size is reduced and the hot air is forced out of the vent in the pole piece. This air flow cools the voice coil. If a relatively low powered amplifier is driven into clipping (to a full square wave for a lot of people), a relatively large portion of the time, the voltage delivered to the voice coil no longer resembles a sine wave as it would with an unclipped signal. While the amplifier's output is clipped, the voice coil is not being motivated to move as far as it should for the power that's being delivered to it and therefore is likely not being cooled sufficiently (since the speaker is driven by a linear motor, the voltage applied to the voice coil determines how far the voice coil moves from its point of rest). At points a, b, d, e, f and h the voltage is changing causing the voice coil to move in the gap and therefore pull in fresh cool air. At points c and g, the voice coil may still be moving a little due to momentum but may not be moving enough to cool properly. Remember that during the clipped portion of the waveform current is still flowing through the voice coil. Since the displacement of the voice coil (and therefore the airflow around the voice coil) is no longer proportional to the heat being generated, the voice coil can overheat. This excess heat may cause the voice coil former to be physically distorted and/or melt the insulation off of the voice coil wire and/or cause the adhesives to fail (especially if the speaker is rated to handle no more than the power that the amp can produce cleanly). If your speakers are rated (honestly) to handle the maximum 'clean' power that your amplifier can produce, slight clipping isn't generally a problem. Severe clipping is more likely to cause a problem. Severe Clipping (square wave):
It always amazes me when I hear some idiot driving down the road and the audio is clearly distorted (is that possible

. Many people drive their amplifiers into what could be called a square wave output (white line below). When an amplifier is pushed that hard, it is actually possible to drive the speaker with twice as much power as the amplifier can cleanly produce into the speaker. As you can see below, the yellow sine wave is the maximum 'clean' output that the amp can produce. When an amplifier is pushed way too hard, the signal will eventually look like the white line. The effective voltage of the white line is ~1.414 x the yellow line. This means the the total power driven into the speaker by the clipped (square wave) signal is double the power delivered by the 'clean' signal (yellow line). This means that the power is double but the cooling of the voice coil will not increase in proportion with the power increase (since the voice coil isn't moving as much as it needs to be for the given power dissipation). This will lead to the voice coil overheating. If we compared the output of a 100 watt amp (the one that's clipping) to a 200 watt amp, the 200 watt amplifier would be able to push the speaker as much as 40% farther than the 100 watt amp (depending on the frequency of the signal). This extra travel (in each direction from its point of rest) would result in added airflow around the voice coil.
Note:
If your speakers are capable of handling significantly more than your amplifier can produce, driving them with a clipped signal will not likely hurt them.
If the speakers can handle 3 or 4 times the power that your amplifier can produce, there's virtually no way to damage your speakers (no matter how clipped the signal is).
If your speakers are rated for the same power handling as your amplifier is capable of producing cleanly, driving them with a clipped signal for extended periods of time may cause speaker damage and/or premature failure.
If your speakers are rated for the same power handling as your amplifier is capable of producing cleanly, driving them with a square wave signal for extended periods of time will likely cause speaker damage.
Thanks Eatel...