There is no one answer to this. IME the need for an external amplifier is generally overblown; people always think "bigger is better". Most people do not know how much power they actually need; again IME they tend to greatly overestimate their average power use, but underestimate the peak ratio. You can look at an SPL calculator like this to get a rough idea how much power you use:
http://myhometheater.homestead.com/splcalculator.html -- to me, 80 dB average is very loud and I am closer to 70 dB. I think a lot of people are only using a watt or two on average, so an AVR that can produce peaks of ~50-100 W is plenty. But it depends upon the speakers, how far away they are from them, room treatment (if any), and preferred loudness (etc.) A speaker's "recommended power" is almost meaningless as the need depends very much on your specific requirements.
Besides pure power (watt) needs, an external amp
may offer lower output impedance, which might provide better frequency response with your speakers since the amp acts more like a pure (ideal) voltage source. That depends upon the speaker's impedance, and a better amp that provides flatter response may or may not be something you like; it can change the frequency response, but even if the change is more accurate, you might not like it as much. There is an ASR article on that, see the link to techie articles in my signature. For SS amps, the difference tends to be minimal, as the output impedance is low enough to drive almost any speaker without significant deviation.
Noise (SNR) is another factor that can matter. If you have highly-sensitive speakers, they will be more sensitive to noise from the signal chain, including the amplifier (which tends to have the lowest SNR of the components in the audio chain). Many folk have added a powerful amplifier only to find that, not only do they not really need all that power, but the added power comes with higher noise.
Bias leads people to believe the sound is better with a bigger amp. By and large blind testing is needed to prove or disprove that. Most people, when they get an amp, expect improvement and so that is what they hear. They also tend to listen louder, especially at first, and louder does sound better so they immediately decide the amp improved things even though turning their AVR up a hair would achieve the same effect.
There are cases where an amp can help, such as speakers that are very insensitive, have very low impedance, or both. But I tend to think the majority of amplifiers added to AVRs are due to marketing and desire rather than real need.
IME/IMO/FWIWFM/etc. - Don