Several threads have discussed matching amps and loudspeakers without really explaining what that means and so I thought I would offer up a little (very little) insight for those who haven't a clue as to what this might involve. Not being a technogeek, feel free to expand or correct this thread where needed or desirable.

It's agonizing enough to simply select a loudspeaker that you like and nobody wants to have to worry about anything other than whether or not the darn things sound good. If they sound good, wrap 'em up, put 'em in the boxes and hold the door open for me.

Two measurements are presented for consideration when partnering the speakers. The first is "sensitivity."
Sensitivity refers to how loud the speaker will sound and is typically measured in decibels from a distance of one meter powered by one watt. A speaker rated at 88db will produce a sound pressure level of 88 decibels at a distance of one meter and powered by 1 watt. A speaker rated at 84db will produce a sound pressure level of 84db and so on...

Most dynamic drive speakers (your average cone style speaker) will range somewhere between 83 and 91 with a much smaller number extending above or below.

In order to increase the sound pressure level by 3db, the amplifier is required to double its output of power in watts. For example, a speaker with a sensitivity rating of 84 producing 84db of sound with 1 watt needs 2 watts to produce a spl of 87db, 4 watts to produce 90db, 8 watts to produce 93db, 16 watts to produce 96db, 32 watts to produce 99db, 64 watts to produce 102db and so on.

On the other hand, a speaker with a sensitivity rating of 91 will produce a spl of 91db at 1 meter with 1 watt of power from the amp, 94db with 2 watts, 97 with 4 watts, 100 with 8 watts, 103 with 16 watts, 106 with 32 watts and 109db with 64 watts.

The second measurement that comes in to play is a speakers impedence. This describes how difficult the speaker is to drive and how much current the speaker will require from the amplifier. Typical speakers are rated between 4 and 8 ohms. In general, the 8 ohm speaker will be easier for the amplifier to drive while the 4 ohm speaker will present a more difficult load on the amplifier. This is especially true when the actual impedence drops lower than 4 ohms at several points in the frequency band. You might think of this as like walking against a head wind, the stronger the wind, the harder you have to work to move forward. Clearly, making note of the amplifiers output rating at both 8 ohms and 4 ohms is needed to determine suitability with your speakers. An amplifier rated at 60 watts rms into an 8 ohm load and 90 watts into a 4 ohm load indicates the ability to increase needed power under difficult loads. Most quality amps will have this ability and the higher the output into a 4 ohm load the better. This is usually referred to as a 'high current' design.

To illustrate partnering speakers and amps, let's look at two scenarios. The first guy is 55 years old and normally listens to music at no higher than 85 decibels at the listening position, which is 3 meters from his speakers in an average size room. His speakers have a sensitivity rating of 85db as meaured from a distance of 1 meter with 1 watt of power. His choices in amplification are almost limitless as he requires very little power to produce adequate sound pressure levels. His choice of speakers is limitless as well since even difficult to drive speakers aren't likely to be driven hard enough to present problems to his amplifier. In fact, this guy may well find a 10 watt triode tube amp to do everything he needs.

The second guy is 27 years old and loves to rock and has a new house with a huge living area that he wants to fill with a powerful sound. This guy demands sound pressure levels that peak around 105 decibels and wants real audiophile quality reproduction.

This guy buys a pair of 3 way floorstanders rated at 88db and 6 ohms. Since his room is large, he listens from a distance of 4 meters. Calculating his amplifier requirements would go something like this: 88db with 1 watt of power at 1 meter, 91 db with 2 watts, 94 with 4 watts, 97 with 8 watts, 100 with 16 watts, 103 with 32 watts, 106 with 64 watts.

If this guy listened at a distance of 1 meter he would need an amp capable of producing 64 watts to reach the sound pressure level he demands. But, he has a large room and listens from further than 1 meter and since music is dynamic in nature, he has to provide for an extra 6db of headroom to capture the peaks in the music or else the sound will flatten as the dynamics increase. Music isn't communicated as a constant tone, it gets louder and softer, producing peaks in the sound pressure level.

Since amplifier power must double to increase the spl by 3db, this guy might need over 200 watts of power to be satisfied.

None of this takes into account the quality of amplification, but rather the necessary requirements to properly match speakers with amplification.

Finally, the "other" measurement to consider is the speakers power handling ability. A speaker rated to handle 80 watts will immediately fail in the second guy's system.

The real problems with amp and speaker compatibility occur when low sensitivity speakers (85 or less) with an impedence of 4 ohms (that actually dip below 4 ohms) are partnered with low quality amps with the expectation of playing them at loud levels. The amp simply runs out of juice trying to keep up, gets hot, distorts the sound and either blows a driver in the speaker or shuts down to avoid over-heating. Even if this worst case scenario doesn't occur, the quality of sound reproduction is almost always bad.

If you consider that the first guy needs very little power to achieve acceptable sound levels, you can appreciate his ability to go after quality rather than quantity. In fact, a high powered amp in his system would make volume control very sensitive and outside the optimum range. This could actually degrade the sound quality in some instances.
The second guy is going to have to spend a big chunk of his budget on watts as well as quality.

There are of course many other considerations in partnering amps with speakers. However, choosing quality products, even entry level products, lessens the likelihood of running into serious compatability problems, though personal tastes will always exist.

This should illustrate the need of knowing how loud you like to listen, where the speakers are going to be located in the room and where your listening position is going to be. A good rule of thumb is to determine how much amplification you need and then double it to provide flexibility and a little headroom. However, tube gear usually has larger power reserves and tend to sound more powerful than their rating might indicate. This is why you might sometimes read a recommendation of "25 watt minimum solid state or 20 tube watts."