1) Most ordinary solid-state amps put out more than enough power for most ordinary speakers.
2) SET amps need high efficiency speakers to attain the loudness most audiophiles want.
Over the years, I have tried to gather enough data to make those vague rules more specific. It is complicated (isn't everything?!) by the notion of headroom. Loudness is measured typically as a short-term average, over something like 1/4 second. But the instantaneous peak power, for example hitting a drum, or the initial impulse of a guitar or piano, is much greater. For well-recorded music, the initial impulses are about 25 times more power than the peak you see on the loudness meter. That's about 14dB headroom. So if you listen at a level that gives measured peaks of 82dB, you need an instantaneous peak of 96dB if you do not want to hear clipping distortion. I chose 82dB because that is typical of the level used by recording engineers. Movies typically need 6dB (four times as much, i.e. 102dB). The THX standard for movie theaters calls for peak levels of 102dB per channel, which is consistent with the recording engineer levels. Some 20 years ago, I gathered a bunch of speaker reviews from Stereophile, which give a minimum-power rating and the speaker sensitivity. I got the same number (102dB peaks) again. So I think that 102dB peaks is enough for most audiophiles, most of the time, and 96dB peaks are enough for the average audiophile. These numbers are somewhat affected by room acoustics (size and absorption), and more strongly affected by your personal preferences and choice of music.
Amplifier power is most usefully expressed in dB, which can be added to the speaker sensitivity to get the peak level. Here's a short table:
1 watt = 0dB
2 watts = 3dB
4 watts = 6dB
8 watts = 9dB
16 watts = 12dB
32 watts = 15dB
64 watts = 18dB
So for example an 86dB speaker needs 10 to 40 watts to obtain undistorted peaks of 96 to 102dB.
These rules are quite flexible, of course. I have two systems in my own home, the music system has 101dB speakers with 8-watt amplifiers (110dB peaks) and the movie system in another room has 89dB speaker with a 2-watt amp (92dB peaks). Both are quite satisfactory to us, for the sounds we listen to.
I know that is a lot to take in, and it's still over-simplified, but I hope that is at least some help!