Speaker and amp pairing

b c are certainly correct, a is not wrong but not the right way to think about it

but there is more nuance and details to it than just that if you want to optimize the match between speaker and amp

You want to pair speakers that sound good with amps that sound good. Limit your speakers to at least 92dB sensitivity and just about any power will do.

Or you can spiral down the rabbit hole. Just know it goes so deep Arne Saaknussem gave up. 

Here’s how I think of speaker sizing and amp matching:

1. how big is the room - size the speakers accordingly
2. how loud do you like to listen - speaker sensitivity and thus amp power should be able to produce the desired db/SPL (can check with any calculator)
3. what’s the nominal impedance of the speakers’ bass woofers and midwoofers? This is a function of the size and number of the drivers, and the crossover topology. Generally, for a standard 2-way with 6.5" driver, the impedance will drop to 3-4ohms at its lowest points even if rated 8ohm nominal. If nominal impedance is 4ohms, well, it’s likely to drop even lower. Be very careful about the current demands for 4ohm nominal speakers - look at the amp design and specs and it should be easy enough to say a NAD 3020 or flea-powered tube amp is going to have a bad time.

Assuming there are no technical red flags, the rest is timbral matching and sonic preferences.

If you aren't absorbed into the tube vs solid state thing, just buy a larger 100W to 150W per channel solid state amp from a reputable audio brand and you should be okay.  Even new NAD and Yamaha larger amps sound okay vs older amps from 20 years ago.  A good 100W/ch amp will drive even lower sensitivity speakers.  Class A/B generally sounds better for the money, due to the larger linear power supply.  Usually lots of used integrated amps (preamp + amp together) for sale here which often offer larger output than receivers which can focus on features you may not need (bluetooth, airplay, etc).  A $500 used integrated from the last few years would be much better sounding than a new $500 (entry level) denon receiver.  
Brad 

There are lots of variables in play, but I learned a long time ago that not all watts are created equal, and that the measured specs for many amplifiers don't tell the whole story about how well they'll actually drive a speaker.  Nor the do specs indicate how an amp will sound.  Some of that is due to the fact that speaker impedances vary a lot, but most don't pose an unusually difficult load for a decent amp. 

If the nominal speaker impedance is rated at 8 ohms, most speakers will do fine with a well designed amp that has good current flow, unless the speaker is known to have a very low or complex impedance.  If nominal impedance is 4 ohms, you'll want an amp that control a low impedance speaker well.  It shouldn't be too difficult to research if any speakers you're interested in are known to to pose very low and/or difficult to drive loads, or how well a particular amp handles more difficult loads.  

As long as a few minimum impedance requirements are considered, I've always tended to focus more on how the speakers and amp sound together, with more focus on the speakers first, then try to find an amp that's capable and that I like the sound of.  It can take time, and trial and error, but can always bring a lifetime of enjoyment when done well.  

I just switched from a 50 watt a/b amp for a 150 watt Class D amp at 8 ohms. My speakers are 4 ohms and this amp will provide 250 watts.
my room is  small 12x14’ and not at loud levels. The higher power amp provides lots of clean power - bass so clean and accurate and zero heat!
not my first class D amp-

you have to listen ! And with the absence of audio salons , a good choice is impossible via mail order! I sent back the 50 watt/ ch amp and it’s a PIA  and only by luck did the next amp sync!

millercarbon and knotscott make the most sense here. Impedance, watts, sensitivity, etc., all come into play. Looking at those numbers and pairing with an amp certainly come into play. However, numbers are that,,,just numbers.
An example....Years ago I was playing Klipsch speakers(Reference line) through a not lower line HK receiver. Watts and all those numbers seemed compatible. The sound to me (in those days) was pretty good. Then, I got a good deal on a NAD integrated and hooked them up to those Klipsch speakers. Sounded like I threw 3 Army blankets over each speaker. Not wanting to ditch the NAD amp I investigated other speakers. PSB was the final result. I believe the two companies are, or were combined.
The main point here is that no matter how long you compare and try to match numbers, there is no final answer until the speakers and amp together are listened.

Whilst giving a greater choice of amplifier the problem with choosing speakers only above 92dB is that severely limits your choice, of speakers. In the old days our choice of computer was often limited by the amount of storage and RAM today both are cheap.  Today watts are cheap too. A Peachtree Decco 125 will drive anything, sounds very nice too. Go up market and a Naim Nait XS 3 at 70 watts will drive virtually anything, a Cambridge Audio CXA 81 at 80 watts also will at half the price. Speakers at 92dB however choice is limited, Klipsch, not a fan (that's me being diplomatic), Focal may squeeze in at 91 dB ( however they are very bright) others at that rating tend to have horns, think listening to music thru a megaphone and or be very expensive see Tannoy, of course you can have a Zu audio product complete with whizzer at 110dB, great for those who like Harleys but better off with a BMW, Yamaha or Ducati if you actually like motorcycling.  Your are not going to find any from Dynaudio, B+W, or my favourite Audio Physics and many other brands. Pick speakers you like then buy an amp that will power it, plenty of speakers at 86+ dB to choose from, hundreds of amps about to power them.

I'm with Henry. I don't get the obsession with sensitivity, especially when transducer engineers often deliberately choose a lower sensitivity driver set to get improved bandwidth performance.  It should be noted sensitivity is relevant only in passives.  Most actives can play as loud as you care to listen, leaving the efficiency argument behind.    

I'm with the last two posters. With modern amps, sensitivity is wholly irrelevant.

Some speakers are very revealing, like ESL's or magnetic planars. Only a very clean amp will sound good with those speakers, but fortunately, these are not hard to find. Your ears will tell you immediately if the amp is the right fit for the speaker. Any dealer should be able to point you in the right direction.

Oh, and ignore specifications. As Jonas Miller (of M&K fame) used to say, "The best audio analyzers possible are your ears."

sensitivity, response, sonic end product, physical end product, cost -- it is all about a fairly complex set of tradeoffs folks

High sensitivity speakers including big horns as I use always have more life like dynamics, immediacy and realism to me.

Some nice thoughts here - thanks so much!

Tonal profile, sensitivity, impedance and recommended power rating are largely what you need to consider though recommended power rating is less of a concern than you might think.

all of this needs to be taken in context of your room and your taste.

Impedance is a critical factor and can’t be ignored.  The lower the impedance, the more current is required to drive a speaker she effectively, the harder it is to drive.  You should find the minimum impedance of the speaker and make sure your amp is at least stable at that level.  If you listen loud, make sure it thrives at that level.  
I had speakers that had a minimum impedance of 1.7ohms and amps that were not rated for that impedance.  Blew lots of fuses.  My sales rep at the time was a jackass and I new nothing as I was seventeen.  

Regarding sensitivity, I have nine pairs of speakers, one has a sensitivity above 92dB.  This is one persons very specific view on sensitivity and affinity for a specific manufacturer.  Millions of people have lower sensitivity speakers and are perfectly happy.  That being said, the lower the sensitivity, the lower the volume output in relative terms so you will need more power which can be limiting depending on your room.  
Regarding power rating, minimum is more important than max unless you listen very loudly for a long stretch.  

Under powering a speaker will leave the sound thin and lead to clipping and distortion.  In extreme cases, this will cause the voice coil to get extremely hot and expand and will lead to a permanent rattle and require driver replacement.  This is uncommon.  
This is driven by room size and proximity to the speakers based on sensitivity. I sell speakers that literally have a power rating range of 25w to like 800w. What do you buy?  Depends on the room and your listening habits.   
You have to pick right speaker for the right room and then power it based on your tastes.  Simple concept and if you are honest with yourself about what you want/need, you will be very happy.  
 

My .02 Depending on your budget and your passion for the music. There are hi rez speakers out there that require component matching to get their best sound, also try to find 3rd party measurements of speakers because most companies fudge the sensitivity numbers. Too much power is always better than to little and again...

I’m running to sets of speakers one is 92 and the other is 87dBSPL @ 2.83v

 Using a Peachtree nova 150- lots of power  both sets of speakers do well with this amplifier.

Do not skimp on power - what a difference

Try EPOS  speakers efficient and very clear !

I tried a Schiit Vidar amp with my KEF Reference 204/2C center speaker, but it didn't blend well with KEF Reference 1 mains driven by an Ayre KV-5 Twenty. Substituting a Parasound JC 1 achieves a seamless blend. I had 3 JC 1s I planed to sell; now I have only 2.

Great info here. I recently purchased a cxa81 and really want the ML Motion 40i. 92db 4ohm. Will this amp's life be shortened by driving these speakers and will it perform adequately?

JMO, but I just bought a different amp that I always wanted to replace an amp that was still doing good after all these years but moved it to a den system. Both good quality amps.

Could tell NO difference in sound coming out of the speakers.

I'm in the camp that as long as the components are of decent quality there isn't going to be that much difference in sound for the average listener.