The following is my engineering interpretation of power cord contribution to good sound. If you have to ask, then I also didn't think they'll make a difference, but reality strikes, my friend!
I've heard amps distorting big time with certain (expensive!) power cord while other amps sounded great with the same. Nothing wrong with either amp!
So why is it?
If you interpret power cords as extension of the "miles and miles" of Romex, inevitably it sounds real dumb that they'll make any difference.
Here is what they are: they are the piece of wire that is closest to your equipment. BIG DIFFERENCE.
Why?
Because audio equipment is affected by NOISE. It's supposed to amplify 20 Hz to 20 KHz, but the circuit doesn't know that!
Audio circuits pick up radio frequency and "mix" it with the audio. This is no technical mumbo-jumbo. Just ask any RF engineer about intermodulation with circuit non-linearity and they'll pull a stack of papers on the topic. Very scientific.
The "funny" thing about radio frequency is that it radiates from antennas and picked up by antennas. The antenna has to be related to the wavelength of the RF emmisions, so short wires are almost "perfect" for that. Yucks!
Well, you might say, there is no short wire. It's an extension of miles and miles. Not so!
When it comes to very high frequencies, the wire's miniscule inductance (very scientific - check technical specs!) is large enough to make the far end of it irrelevant. That's a great simplification, of course, unless one wants to solve Heavyside/Maxwell equations. I don't recommend that...
Now that we understand the nature of wires in close proximity, perhaps we'll be more open-minded about the effects of these wires on the system.
Now, those of you in the rural area might think that they don't have RF pollution to worry about... Wrong!
Guess what. The power supply in any equipment is a source of RF noise. Ahh?! Say what?!
If you have a high speed scope, pull it out and sample (at your own risk!!!!!!!!!!!!!!!!) the rectifier diodes at the switching point. Zoom in and enjoy the view!
There are several mechanisms in which RF pickup muddies audio. One was mentioned above - direct mixing. The most common might be the impact on jitter in digital audio sources. RF has its nasty ways of leaking through stray capacitance. In average equipment it takes very little effort to reach clock circuits and add a few nanoseconds of "fuzziness" to your timing reference. This topic has been analyzed to great boredom, so just search for exact details. The jist of it is that very few nanoseconds of jitter are enough to cause distortion of the non-harmonic type - the worst there is. Audible products that do not relate to the music tones!
If you don't accept that jitter is an issue then you are seriously wasting your time reading all the way to this point. It's too scientific, perhaps.
So now we understand three things:
1) short wires in close proximity to the equipment differ from miles of Romex in regard to RF rejection (elementary Physics).
2) Any system with a power supply emmits RF. (you can verify this yourself - again: at your own risk!!!!!)
3) Low levels of RF mixed with audio are not nice. (Just ask any RF engineer)
Any more comments about the "myth" of power cords?!
Mind you, I don't advocate paying $2,000 for these, but at least be aware that they are doing something other than draining your bank account. Some power cords do RF filtering extremely well!