Originally posted by awalbert88 Underpowering the sub will never hurt it. Overpowering the sub might hurt it, depending on the quality of the sub and the degree to which you overpower it.
That being said, the amp's build quality is far more important than the sub rating. For example, if you have a JBL 300.1 (300x1 @ 2ohm) and a JL 13W7 (1000W dual 1.5ohm), and you crank the gain on the 300.1 all the way up and push your HU volume to max, the amp is going to begin clipping, which will send very loud, very high tones through to the sub, which WILL damage it. If you push an amp too hard, and it starts to clip, then the quality of the sub becomes irrelevant, because it won't take long to destroy it that way. However, if you have a powerful amp (say, the Zapco 4kW model) and a relatively weak sub (JL 6W0 - 75w), and you turn the gain on the Zapco all the way down to where it is barely pushing any power, then the sub should be fine, and in fact would sound better than if a 75w amp were driving it, because the 75w amp would be running at full power, thus more likely to distort or overheat. So, more power is almost always better so long as you use it correctly.
Please feel free to correct me if I'm wrong on any of this, but I believe I have it correct.