power

This is a key problem with speakers - especially audiophile designs. At higher levels they compress and sound dull and flat. It is a problem in Xmax excursion of the drivers as well as overheating issues prevalent in small voice coils (less than 4 inch diameter). It is extremely expensive to make good drivers that still sound great when pushed hard and therefore designers most often choose cheaper parts (cheaper speaker parts can still sound great at lower levels but the sound falls apart when really pushed). Note that speaker efficiency is only measured at 1 watt so it does not tell you if the speaker can play very loud cleanly (lower efficiency designs with better parts may play much louder than high efficiency designs with cheap parts).

A very powerful amplifier is actually safer for the speaker as clipping at lower power can damage tweeters more quickly than clean signals at higher power. As Falconquest notes above - 4ohm speakers are much harder to drive than 8 ohm and will benefit from a beefy amplifier that can handle extreme levels of current necessitated by the very low impedance....

Soundstage speaker measurements show a test at 90 dB and at 95 dB and many audiophile designs show compression and high distortion levels at a mere 95 dB - so transients more often than not are a problem that the amplifier cannot fix as it is an inherent limitation of the accuracy of the speakers themselves. Here I am referring to high end audiophile favourite designs like Wilson etc.

Also something to keep in mind looking at amps, not all watts are "created equal". Make sure the amp you're looking at has a stiff well designed power supply not just a high enough watt rating.

@shadorne 

I have no idea what you're talking about with speakers showing compression at a couple of watts. It looks like you're just throwing silliness out there with no context to buttress nonsensical ideas. 

As for power supplies, they're a huge expense in an amp, and a lot of folks won't drop a power supply into an amp that will supply more power than the outputs will push into 4 ohm. The little 37.5 watt amp I built has a supply in it that'll belt out 400 watts and it sounds like it. Aside from the risk of melting the outputs, that power supply is the only real limit to what the amp will produce. 

@kost_amojan

Not sure where I said 2 watts. Speaker drivers have an Xmax after which they are nonlinear and compress dynamics.

Speaker voice coil could run at 100 degrees and may be rated up to 200 degrees. 98% of power into a voice coil is dissipated as heat.

Your knowledge of Amps may be outstanding. However many or most people have a lack of understanding of speakers and make the mistake of treating them like linear devices with no power handling issues....

If your speakers compress at all within normal listening levels (i.e. other than the ear damage zone) you have crappy speakers and/or a crappy amp. Also the thing with amps sounding good is the overall design which should produce a great sounding "first watt" and the following watts are simply gravy. The speaker impedance and efficiency will pretty much tell you most of what you need to know about matching an amp to speakers, but it's gotta sound good to YOU. I've designed (and mixed with) systems for live sound using multi thousand watt amps and speaker systems that in terms of efficiency and power handling make home audio gear look weak and silly, but in my active listening home rig I use a 12 watt per side single ended Class A amp with reasonably efficient mains and a couple of powered subs…it will play louder than I need it to and sound sublime with any either calm or dynamic music I put through it because it's supposed to.