Keep in mind there is a difference between actually overpowering, and simply having a larger than recommended amp on them. A 200w amp will not put out 200w constantly; it's highly dependent upon volume level, how the gain is set, type of music, recording level of the music, etc etc. So, just because someone has a 200w amp (for example) on their speakers, it doesn't mean their speakers are ever actually seeing the full 200w, atleast for anything longer than .1 seconds.
Then you have to issue of how the speaker's power handling was actually rated. Whether it's conservative, if it's the thermal limit or just the suggested power, etc etc.
1) Thermal failure; you exceed the thermal power handling limits of the driver.
2) Mechanical failure; You exceed the mechanical limits of the driver, which causes physical damage (such as bottoming out the driver, ripping the spider, ripping a tinsel lead, etc etc)
3) Physical damage/manufacturer defect; things like misaligned coils, dropping the speaker, etc etc.