Is there such a thing as too much power?

I like cars...let's go back to the car analogy.

A Porsche GT2 sold to a person that is legal on the street has to be de-tuned to race.  However, horsepower isn't breaking or handling and a high horsepower car without a good breaking and suspension system is limited to being fast in a straight line or in other words drag racing.

A Miata with the right driver can challenge many high horsepower cars because its light weight and balance. 

Not all amplifiers have the same circuitry and components and may not excel in reproducing all types of music...they could be great at a tornado warning not music.

I recently upgraded from a 70 W tube amp to a 500 W solid-state. No comparison, more watts are better. In my opinion ,flea watt amps are interesting and can sound amazing with horns or point source whizzers, but for the large  majority of speakers more power is Better.

The SPL of your speakers are important. Much of the time, under normal listening volumes, you may be using only 1-2 watts. The quality of the wattage, not the overall power, dictates listening happiness. Unless you have big lawn parties with huge inefficient speakers 300 watts is overkill. 

+1 for Cakyol, Mapman,Arctikdeth,Atmasphere and others.  High current amps are what is needed, not necessarily high wattage amps, unless you’re pushing high efficiency horn loaded speakers, or something like them, although they usually go hand in hand.  Dynamic headroom is the main reason for a high powered amp. I’ve never heard it, but it’s said, to reproduce the cannon shot in the 1812 Overture, an amp needs 700+ watts to reproduce it.  I play many difference genres of music, sometimes at high dB levels.  This is when the extra power comes into play.  I love class “A” biased amps.  They’re quick to reproduce the music and it sounds amazing.  This is not to say that a smaller tube amp feeding high efficiency speakers isn’t happening.  Even a warm SS amp will suffice.  For my tastes, I prefer the hefty class A amp.  
We all have our preferences.

Atmasphere, Is there a way to determine an amplifier's lowest point of distortion apriori or is an empirical issue?

A personal observation:  I have a very powerful solid state amplifier and a small tube amp  (over 1000W vs. 10W)  and I've recently discovered I prefer the sound of the big amp over the little one with my very efficient speakers (>99db).  I recognize that there are a lot of variables at play here.